SSC CGL Triangles MCQs| Powerful Practice Questions

SSC CGL Triangles MCQs 5SSC CGL Triangles MCQs with 20 exam-oriented questions, answers, detailed explanations, and shortcut tricks for Tier-I and Tier-II preparation

SSC CGL Triangles MCQs

1. The angles of a triangle are in the ratio 2 : 3 : 4. The largest angle is

A) 60°  B) 70°

C) 80°  D) 90°

Correct Answer: C) 80°

Explanation:

Sum of angles of a triangle = 180°

Total parts = 2 + 3 + 4 = 9

One part = 180°/9 = 20°

Angles are 2 × 20 = 40; 3 × 20 = 60; 4 × 20 = 80

Largest angle = 4 × 20° = 80°

2. In ΔABC, ∠A = 55° and ∠B = 65°. The exterior angle at C is

A) 110°  B) 115°

C) 120°  D) 125°

Correct Answer: C) 120°

Explanation:

Exterior angle = Sum of its opposite interior angles

= ∠A + ∠B

= 55° + 65°

= 120°

3 In an isosceles triangle, the unequal angle is 40°. Each equal angle is

A) 60°  B) 65°

C) 70°  D) 75°

Correct Answer: C) 70°

Explanation:

Equal angles = x

2x + 40° = 180°

2x = 140°

x = 70°

4. The hypotenuse of a right-angled triangle is 13 cm and one side is 5 cm. The other side is

A) 10 cm  B) 11 cm

C) 12 cm  D) 14 cm

Correct Answer: C) 12 cm

Explanation:

By Pythagoras theorem

13² = 5² + x²

169 = 25 + x²

x² = 144

x = 12 cm

5. The area of an equilateral triangle is 144√3 cm². Its side is

A) 12 cm  B) 18 cm

C) 24 cm  D) 36 cm

Correct Answer: C) 24 cm

Explanation:

Area of equilateral triangle =   a²

144 √3=  a²

a² = 576

a = 24 cm

6. Two similar triangles have corresponding sides in the ratio 3 : 5. The ratio of their areas is

A) 3 : 5  B) 6 : 10

C) 9 : 25  D) 27 : 125

Correct Answer: C) 9 : 25

Explanation

For similar triangles

Ratio of areas = Square of the ratio of corresponding sides.

A₁/A₂ = (3/5 )²

= 9/25

A₁:A₂ = 9 : 25

7. Two similar triangles have areas 64 cm² and 100 cm². The ratio of their corresponding sides is

A) 4 : 5  B) 8 : 10

C) 16 : 25  D) 3 : 4

Correct Answer: A) 4 : 5

Explanation:

  Ratio of corresponding sides

Ratio of corresponding sides = 4 : 5

8. In ΔABC, AB = 7 cm, AC = 9 cm, and BC = 8 cm. The median drawn to side BC divides BC into

A) 2 cm and 6 cm       B) 3 cm and 5 cm

C) 4 cm and 4 cm      D) 1 cm and 7 cm

Correct Answer: C) 4 cm and 4 cm

Explanation:

A median always divides the opposite side into two equal parts

BC = 8 cm

Each part = 8/2 = 4 cm

9. The centroid of a triangle divides each median in the ratio

A) 1 : 1  B) 1 : 2

C) 2 : 1  D) 3 : 1

Correct Answer: C) 2 : 1

Explanation:

The centroid divides every median in the ratio 2 : 1

The longer portion lies between the vertex and centroid

Shortcut: Remember Centroid = 2 : 1

10. A right-angled triangle has sides 6 cm, 8 cm and 10 cm. Its inradius is

A) 1 cm  B) 2 cm

C) 3 cm  D) 4 cm

Correct Answer: B) 2 cm

Explanation:

For a right triangle

r= (a + b – c)/2[

r = (6 + 8 –10)/2

= 4/2 =2

∴ inradius = 2 cm

11. The circumradius of a right-angled triangle whose hypotenuse is 18 cm is

A) 6 cm  B) 9 cm

C) 12 cm  D) 18 cm

Correct Answer: B) 9 cm

Explanation:

In a right-angled triangle, mid- point of hypotenuse is the Circumcentre

Circum Radius = (Length of Hypotenuse)/2

= 18/2 = 9

12. Which of the following can form a triangle?

A) 2 cm, 3 cm, 6 cm         B) 4 cm, 5 cm, 10 cm

C) 5 cm, 6 cm, 10 cm       D) 1 cm, 2 cm, 4 cm

Correct Answer: C) 5 cm, 6 cm, 10 cm

Explanation:

For a triangle: Sum of any two sides of a tringle is greater than the third side

For option C: 5 + 6 > 10; 6 + 10 > 5 ; 5 + 10 > 6

Therefore, it can form a triangle

13.In ΔABC, AD bisects ∠A. If AB = 6 cm, AC = 9 cm and BC = 10 cm, then BD : DC is

A) 2 : 3  B) 3 : 2

C) 1 : 2  D) 2 : 1

Correct Answer: A) 2 : 3

Explanation:

BD/DC = AB/AC

= 6/9

= 2/3

∴ BD : DC = 2 : 3

14. The base of a triangle is 18 cm and its height is 14 cm. Its area is

A) 112 cm²  B) 126 cm²

C) 144 cm²  D) 252 cm²

Correct Answer: B) 126 cm²

Explanation:

Area   = 1/2  (base)× (height)

= 1/2 (18 ×14)

=9×14 =126 cm²

15. The sides of a triangle are 13 cm, 14 cm and 15 cm. Its area is

A) 72 cm²  B) 84 cm²

C) 96 cm²  D) 105 cm²

Correct Answer: B) 84 cm²

Explanation:

s= (13+14+15)/2=21

∴ Area of triangle = 84 cm²

16. Two similar triangles have corresponding sides in the ratio 2 : 3. If the perimeter of the smaller triangle is 24 cm, the perimeter of the larger triangle is

A) 30 cm  B) 32 cm

C) 36 cm  D) 40 cm

Correct Answer: C) 36 cm

Explanation:

Perimeters of similar triangles are in the same ratio as corresponding sides

24/P= 2/3

P=24 × 3/2=36

∴ 36 cm.

 17. A right-angled triangle has hypotenuse 25 cm and one side 7 cm. Its area is

A) 72 cm²  B) 84 cm²

C) 96 cm²  D) 120 cm²

Correct Answer: B) 84 cm²

Explanation:

x²=25² –7²

=625 – 49 = 576

x = 24 cm.

Area of triangle = 1/2(7 × 24)

= 84(cm)²

18. The height of an equilateral triangle of side 16 cm is

A) 4√3 cm  B) 6√3 cm

C) 8√3 cm  D) 10√3 cm

Correct Answer: C) 8√3 cm

Explanation:

h= (√3/2)a

h= (√3/2)(6)

h= 8√3 cm

19. In a triangle, the angles are 40°, 60° and 80°. Which side is the longest?

A) Side opposite 40°       B) Side opposite 60°

C) Side opposite 80°        D) Cannot be determined

Correct Answer: C) Side opposite 80°

Explanation:

In a triangle, the side opposite the largest angle is the longest

Largest angle = 80°

Therefore, the side opposite 80° is longest

20. A median of a triangle is 18 cm long. The distance of the centroid from the vertex along the median is:

A) 6 cm  B) 9 cm

C) 12 cm  D) 15 cm

Correct Answer: C) 12 cm

Explanation:

Centroid divides median in the ratio 2 : 1

Distance from vertex =  (2/3)×18

Therefore, answer = 12 cm

21. The corresponding sides of two similar triangles are in the ratio 4 : 7. If the area of the smaller triangle is 80 cm², the area of the larger triangle is

A) 140 cm²  B) 210 cm²

C) 245 cm²  D) 280 cm²

Correct Answer: C) 245 cm²

Explanation:

Area ratio =4²:7²=16:49

80/A = 16/49

A=80× [49/16]

=5×49=245

Area of larger triangle = 245 cm²

22. In ΔABC, AB = 8 cm, AC = 12 cm and BC = 15 cm. The angle bisector of ∠A divides BC into two parts. The longer part is

A) 8 cm  B) 9 cm

C) 10 cm  D) 12 cm

Correct Answer: C) 9 cm

Explanation:

By angle bisector theorem:

BD:DC=AB:AC=8:12=2:3

Total parts = 5

BC = 15 cm.

One part = 3 cm.

Longer part = 3 × 3 = 9 cm.

23. Which of the following sets represents a right-angled triangle?

A) 8, 15, 16                       B) 9, 12, 15

C) 10, 12, 14                   D) 12, 16, 21

Correct Answer: B) 9, 12, 15

Explanation:

a²+b² = c²

From option B:  9²+12² = 81+144 = 225 =15²

Therefore, 9, 12, 15 forms a right triangle

24. The point of intersection of the three internal angle bisectors of a triangle is called

A) Centroid                     B) Orthocentre

C) Circumcentre              D) Incentre

Correct Answer: D) Incentre

Explanation:

The point of intersection of the three Medians = Centroid

The point of intersection of the Perpendicular bisectors = Circumcentre

The point of intersection of the three Altitudes = Orthocentre

The point of intersection of the three Angular bisectors = Incentre

25. The sides of a triangle are 10 cm, 17 cm and 21 cm. Its area is

A) 72 cm²  B) 80 cm²

C) 84 cm²  D) 90 cm²

Correct Answer: C) 84 cm²

Explanation:

 s= (10+17+21)/2 =24

SSC CGL Quantitative Aptitude Topics

• Number System
• Decimals
• Fractions
• Percentages
• Ratio & proportion
• Square roots
• Averages
• Interest (simple & compound)
• Profit & loss
• Discount
• Partnerships
• Mixture & Alligation
• Time & speed & distance
• Time & work
• Advanced math includes basic algebraic identities
• Elementary surds
• Linear equations
• Triangles
• Circles
• Regular polygons, right prisms, cones, cylinders, spheres
• Trigonometry

YOUTUBE

If you are interested in reading stories, CLICK HERE