# MCQs for Class 10 Maths Chapter 6 Triangles

MCQs for **Class 10 Maths Chapter 6 Triangles**: In this article, we have covered all the important MCQs for Free for Class 10 Term 1 2021-22 Board Exams. In accordance with the latest pattern, Padhle is here with MCQ Questions for Class 10.

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# MCQs for Class 10 Maths Chapter 6 Triangles

1. O is a point on side PQ of a APQR such that PO = QO = RO, then

(a) RS² = PR × QR

(b) PR² + QR² = PQ²

(c) QR² = QO² + RO²

(d) PO² + RO² = PR²

Answer: (b) PR² + QR² = PQ²

2. D and E are respectively the midpoints on the sides AB and AC of a triangle ABC and BC = 6 cm. If DE || BC, then the length of DE (in cm) is

(a) 2.5

(b) 3

(c) 5

(d) 6

Answer: (b) 3

3. Which of the following triangles have the same side lengths?

(a)Scalene

(b)Isosceles

(c)Equilateral

(d)None of these

Answer: (c) Equilateral

4. In ΔABC, if DE || BC, AD = x, DB = x – 2, AE = x + 2 and EC = x – 1, then value of x is

(a) 3

(b) 4

(c) 5

(d) 3.5

Answer: (b) 4

5. In an equilateral triangle ABC, if AD⊥BC,then

(a) 5AB^{2} = 4AD^{2}.

(b) 4AB^{2} = 3AD^{2}.

(c) 3AB^{2} = 4AD^{2}.

(d) 2AB^{2} = 3AD^{2}.

Answer: (c) 3AB^{2} = 4AD^{2}.

6. In ABC, DE || AB. If CD = 3 cm, EC = 4 cm, BE = 6 cm, then DA is equal to

(a) 7.5 cm

(b) 3 cm

(c) 4.5 cm

(d) 6 cm

Answer: (c) 4.5 cm

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7. In triangle PQR, if PQ = 6 cm, PR = 8 cm, QS = 3 cm, and PS is the bisector of angle QPR, what is the length of SR?

(a) 2

(b) 4

(c) 6

(d) 8

Answer: (b) 4

8. Area of an equilateral triangle with side length a is equal to:

(a)√3/2a

(b)√3/2a^{2}

(c)√3/4 a^{2}

(d)√3/4 a

Answer: (c)√3/4 a2

9. The perimeters of two similar triangles ABC and PQR are 60 cm and 36 cm respectively. If PQ = 9 cm, then AB equals

(a) 6 cm

(b) 10 cm

(c) 15 cm

(d) 24 cm

Answer: (c) 15 cm

10. In a triangle ABC, AC= √180, AB = 6, BC = 12. What is ∠B = ?

(a) 90°

(b) 30°

(c) 45°

(d) 60°

Answer: (a) 90°

11. In a square of side 10 cm, its diagonal = …

(a) 15 cm

(b) 10√2 cm

(c) 20 cm

(d) 12 cm

Answer: (b) 10√2 cm

12. The lengths of the diagonals of a rhombus are 16 cm and 12cm. Then, the length of the side of the rhombus is

(a) 9 cm

(b) 10 cm

(c) 8 cm

(d) 20 cm

Answer:(b) 10cm

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13. The diagonals of a rhombus are 16cm and 12cm, in length. The side of rhombus in length is:

(a)20cm

(b)8cm

(c)10cm

(d)9cm

Answer: (c)10cm

14. If ΔABC is similar to ΔDEF such that 2 AB = DE and BC = 8 cm then EF is equal to.

(a) 12 cm

(b) 4 cm

(c) 16 cm

(d) 8 c

Answer: (c) 16 cm

15. In right triangle ABC right angled at B, a line DE is drawn through the mid point D of AB and parallel to BC. If AB = 9 cm, BC = 12 cm. AE = ?

(a) 13 cm

(b) 10 cm

(c) 8.5 cm

(d) 7.5 cm

Answer: (d) 7.5 cm

16. In a rectangle Length = 8 cm, Breadth = 6 cm. Then its diagonal = …

(a) 9 cm

(b) 14 cm

(c) 10 cm

(d) 12 cm

Answer: (c) 10 cm

17. A flag pole 18 m high casts a shadow 9.6 m long. Find the distance of the top of the pole from the far end of the shadow.

(a) 25.6

(b) 20.4

(c) 23.7

(d) 32.5

Answer:(b) 20.4

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18. Corresponding sides of two similar triangles are in the ratio of 2:3. If the area of small triangle is 48 sq.cm, then the area of large triangle is:

(a)230 sq.cm.

(b)106 sq.cm

(c)107 sq.cm.

(d)108 sq.cm

Answer: (d)108 sq.cm

19. In ΔABC, AB = 6 cm and DE || BC such that AE = 1/4 AC then the length of AD is

(a) 2 cm

(b) 1.2 cm

(c) 1.5 cm

(d) 4 cm

Answer: (c) 1.5 cm

20. If perimeter of a triangle is 100cm and the length of two sides are 30cm and 40cm, the length of third side will be:

(a)30cm

(b)40cm

(c)50cm

(d)60cm

Answer: (a)30cm

21. ΔABC ~ ΔDEF. If AB = 4 cm, BC = 3.5 cm, CA = 2.5 cm and DF = 7.5 cm, then the perimeter of ΔDEF is

(a) 10 cm

(b) 14 cm

(c) 30 cm

(d) 25 cm

Answer: (c) 30 cm

22. If the legs of an isosceles right triangle are 5 cm long, approximate the length of the hypotenuse to the nearest whole number.

(a) 9 cm

(b) 7 cm

(c) 70 cm

(d) 90 cm

Answer: (b) 7 cm.

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23. In a rhombus if d1 = 16 cm, d2 = 12 cm, its area will be…

(a) 16 × 12 cm²

(b) 96 cm²

(c) 8 × 6 cm²

(d) 144 cm²

Answer: (b) 96 cm²

24. Diagonals of a trapezium PQRS intersect each other at the point O, PQ || RS and PQ = 3 RS, Then the ratio of areas of triangles POQ and ROS is:

(a) 1:9

(b) 9:1

(c) 3:1

(d) 1:3

Answer:(b) 9:1

25. If triangles ABC and DEF are similar and AB=4cm, DE=6cm, EF=9cm and FD=12cm, the perimeter of triangle is:

(a)22cm

(b)20cm

(c)21cm

(d)18cm

Answer: (d)18cm

26. ΔDEF ~ ΔABC. If DE : AB = 2 : 3 and ar ΔDEF is equal to 44 square units then ar (ΔABC) (square unit) is

(a) 99

(b) 120

(c) 176/9

(d) 66

Answer: (a) 99

27. A semicircle is drawn on AC. Two chords AB and BC of length 8 cm and 6 cm respectively are drawn in the semicircle. What is the measure of the diameter of the circle?

(a) 14 cm.

(b) 10 cm.

(c) 12 cm.

(d) 11 cm.

Answer: (b) 10 cm

28. If in two As ABC and DEF, AB/DF=BC/FE=CA/ED, then

(a) ∆ABC ~ ∆DEF

(b) ∆ABC ~ ∆EDF

(c) ∆ABC ~ ∆EFD

(d) ∆ABC ~ ∆DFE

Answer: (d) ∆ABC ~ ∆DFE

29. ABCD is a trapezium in which AB|| DC and P, Q are points on ADand BC respectively such that PQ || DC. If PD = 18 cm, BQ = 35 cm andQC = 15 cm, find AD.

(a) 55cm

(b) 57cm

(c) 60cm

(d) 62cm

Answer:(c) 60cm

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30. The height of an equilateral triangle of side 5cm is:

(a)4.33

(b)3.9

(c)5

(d)4

Answer: (a)4.33

31. ΔABC and ΔBDE are two equilateral triangles such that D is the mid point of BC. Ratio of the areas of triangle ΔABC and ΔBDE is.

(a) 2 : 1

(b) 1 : 2

(c) 4 : 1

(d) 1 : 4

Answer: (c) 4 : 1

32. Three numbers form a Pythagorean triplet. Two of them are 15 and 17 where 17 is the largest of them. The third number is

(a) 8

(b) 12

(c) 13

(d) 5

Answer: (a) 8

33. It is given that ∆ABC ~ ∆DEF and BCEF=15. Then Undefined control sequence \operatorname is equal to

(а) 5

(b) 25

(c) 125

(d) 15

Answer: (b) 25

34. Areas of two similar triangles are 36 cm^{2} and 100 cm^{2}. If the length of a side of the larger triangle is 20 cm, then the length of the corresponding side of the smaller triangle is:

(a) 12cm

(b) 13cm

(c) 14cm

(d) 15cm

Answer:(a) 12cm

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35. If ABC and DEF are two triangles and AB/DE=BC/FD, then the two triangles are similar if

(a)∠A=∠F

(b)∠B=∠D

(c)∠A=∠D

(d)∠B=∠E

Answer: (b)∠B=∠D

36. If ΔABC ~ ΔPQR, arΔABC/arΔPQR = 9/4 and AB = 18 cm, then the length of PQ is

(a) 14 cm

(b) 8 cm

(c) 10 cm

(d) 12 cm

Answer: (d) 12 cm

37. D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 3 cm, BD = 5 cm, BC = 12.8 cm and DE || BC. Then length of DE (in cm) is

(a) 4.8 cm

(b) 7.6 cm

(c) 19.2 cm

(d) 2.5 cm

Answer: (a) 4.8 cm

38. D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 2 cm, BD = 3 cm, BC = 7.5 cm and DE || BC. Then, length of DE (in cm) is

(a) 2.5

(b) 3

(c) 5

(d) 6

Answer:(b) 3

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39. If ABCD is parallelogram, P is a point on side BC and DP when produced meets AB produced at L, then select the correct option

(a) DP/BL = DC/PL

(b) DP/PL = DC/BL

(c) DP/PL = BL/DC

(d) DP/PL = AB/DC

Answer: (b) DP/PL = DC/BL

40. Sides of two similar triangles are in the ratio 4: 9. Areas of these triangles are in the ratio

(a)2: 3

(b)4: 9

(c)81: 16

(d)16: 81

Answer: (d)16: 81

41. If the ratio of the perimeters of two similar triangles is 4 : 25, then the ratio of the areas of the similar triangles is

(a) 16 : 625

(b) 2 : 5

(c) 5 : 2

(d) 625 : 16

Answer: (a) 16 : 625

42. In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. The length of the smallest side of the triangle PQR is :

(a) 6 cm

(b) 8 cm

(c) 7 cm

(d) 10 cm

Answer: (b) 8 cm

43. If ΔABC ~ ΔDEF and ΔABC is not similar to ΔDEF then which of the following is not true?

(a) BC.EF = AC.FD

(b) AB.ED = AC.DE

(c) BC.DE = AB.EE

(d) BC.DE = AB.FD

Answer: (c) BC.DE = AB.EE

44. The length of altitude of an equilateral triangle of side 8cm is

(a) √3 cm

(b) 2√3 cm

(c) 3√3 cm

(d) 4√3 cm

Answer:(d) 4√3 cm

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45. ΔPQR is an equilateral triangle with each side of length 2p. If PS ⊥ QR, then PS is equal to

(a) √32p

(b) 2p

(c) √3p

(d) p

Answer: (c) √3p

46. Which of the following is a Pythagorean triplet ?

(a) (36,18,43)

(b) (15,20,25)

(c) (3,12,13)

(d) (24,25,26)

Answer: (b) (15,20,25)

47. If ΔABC ~ ΔPQR, BCQR=13 then Undefined control sequence \operatorname is

(a) 9

(b) 3

(c) 1/3

(d) 1/9

Answer: (a) 9

48. If ΔABC ~ ΔDEF, AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm, find the perimeter of ABC.

(a) 18 cm

(b) 20 cm

(c) 21 cm

(d) 22 cm

Answer:(a) 18 cm

49. In ΔLMN, ∠L = 50° and ∠N = 60°, If ΔLMN ~ ΔPQR, then find ∠Q

(a) 50°

(b) 70°

(c) 60°

(d) 40°

Answer: (b) 70°

50. If the sum of the length of the legs of a right triangle is 49 cm and the hypotenuse is 41 cm, find its shortest side.

(a) 19 cm

(b) 40 cm

(c) 4 cm

(d) 9 cm

Answer:(d) 9 cm

51. If ΔABC ~ ΔQRP, Undefined control sequence \operatorname, AB = 18 cm and BC = 15 cm, then PR is equal to

(a) 10 cm

(b) 12 cm

(c) 203cm

(d) 8 cm

Answer: (a) 10cm

52. A 5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4 m high. If the foot of the ladder is moved 1.6 m towards the wall, then the distance by which the top of the ladder would slide upwards on the wall is:

(a) 2 m

(b) 1.2 m

(c) 0.8 m

(d) 0.5 m

Answer:(c) 0.8 m

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53. PQ = 24 cm, QR = 26 cm ∠PAR = 90°, PA = 6 cm, and AR = 8 cm, the degree measure of ∠QPR is

(a) 90°

(b) 100°

(c) 50°

(d) 45°

Answer: (a) 90°

54. A boy is trying to catch fish sitting at a height of 12 m from the surface of the water. A big fish is at a horizontal distance of 5 m from him. What should be the length of his string to get the fish?

(a) 10

(b) 13

(c) 7

(d) 15

Answer: (b) 13

55. If in triangles ABC and DEF,ABDE=BCFD , then they will be similar, if

(a) ∠B = ∠E

(b) ∠A = ∠D

(c) ∠B = ∠D

(d) ∠A = ∠F

Answer: (c) ∠B = ∠D

56. ΔABC ~ ΔPQR, PM is median of ΔPQR. If ar ΔABC = 289 cm², BC = 17 cm, MR = 6.5 cm then the area of ΔPQM is

(a) 169 cm²

(b) 13 cm²

(c) 84.5 cm²

(d) 144.5 cm²

Answer: (c) 84.5 cm²

57. The length of the side of a rhombus whose diagonals are of lengths 24 cm and 10 cm is

(a) 17 cm.

(b) 14 cm.

(c) 13 cm.

(d) 16 cm.

Answer: (c) 13 cm.

58. ΔACB ~ ΔAPQ. If AB = 6 cm, BC = 8 cm, and PQ = 4 cm then AQ is equal to

(a) 2 cm

(b) 2.5 cm

(c) 3 cm

(d) 3.5 cm

Answer: (c) 3 cm

59. In ΔABC, AB = 5 cm, AC = 7 cm. If AD is the angle bisector of ∠A. Then BD : CD is:

(a) 25 : 49

(b) 49 : 25

(c) 6 : 1

(d) 5 : 7

Answer: (d) 5 : 7

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60. wo isosceles triangles have equal angles and their areas are in the ratio 16 : 25. Then, the ratio of their corresponding heights is

(a) 3/5

(b) 5/4

(c) 5/7

(d) 4/5

Answer: (d) ⅘

61. The monitors of computers are measured along the diagonal. What is the size of the largest monitor that can be placed in a space measuring 17″ x 21″?

(a) 28″

(b) 25″

(c) 26″

(d) 27″

Answer: (d) 27″

62. Three squares are based on the sides of a right angled triangle. The area of the two smaller ones are 144 sq. cm and 256 sq. cm. What is the area of the third one?

(a) 625 sq. cm

(b) 361 sq. cm

(c) 400 sq. cm

(d) 900sq. cm

Answer: (c) 400 sq. cm

63. Triangle ABC is such that AB = 3 cm, BC = 2 cm and CA = 2.5 cm. Triangle DEF is similar to ΔABC. If EF = 4 cm, then the perimeter of ΔDEF is :

(a) 7.5 cm

(b) 15 cm

(c) 22.5 cm

(d) 30 cm

Answer: (b) 15 cm

64. Two friends A and B start from the same point in the Eastern and Northern directions at the same time. How far are they from each other when A has travelled 5 km and B has travelled 12 km. distance?

(a) 8 km

(b) 17 km

(c) 10 km

(d) 13 km

Answer:(d) 13 km

65. The line segments joining the mid points of the sides of a triangle form four triangles each of which is :

(a) Similar to the original triangle

(b) Congruent to the original triangle

(c) An equilateral triangle

(d) An isosceles triangle

Answer: (a) Similar to the original triangle

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