# PRACTICE QUESTIONS ON TRIANGLES

### Examination Questions on Triangles

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1. For a triangle ABC, D and E are two points on AB and AC such that AD = 1/4AB, AE = 1/4AC. If BC = 12 cm then DE is :

1. 3 cm
2. 6 cm
3. 5 cm
4. 4 cm

2. In an acute angled triangle ABC, if sin 2(A + B – C)= 1 and tan(B + C – A) = √3, then the value of angle B is

1. 60°
2. 30°
3. 52 ½°
4. 67 ½°

3. If the in radius of a triangle with perimeter 32 cm is 6 cm, then the area of the triangle in sq. cm is

1. 48
2. 100
3. 64
4. 96

4. ABC is a right angled triangle, B being the right angle. Mid-points of BC and AC are respectively B’ and A’. The ratio of the area of the quadrilateral AA’ B’B to the area of the triangle ABC is

1. 1 : 2
2. 2 : 3
3. 3 : 4
4. None of the above

5. In a triangle ABC, the side BC is extended up to D. Such that CD = AC, if angle BAD = 109° and angle ACB = 72° then the value of angle ABC is

1. 35°
2. 60°
3. 40°
4. 45°

6. Side BC of triangle ABC is produced to D. If angle ACD = 140o and angle ABC = 3 ⁄BAC, then find angle A.

1. 45°
2. 55°
3. 35°
4. 60°

7. If O be the circum centre of a triangle PQR and angle QOR = 110°, angle OPR = 25°, then the measure of angle PRQ is

1. 55°
2. 60°
3. 65°
4. 50°

8. D and E are mid-points of AB and AC of triangle ABC. If angle A = 80o, angle C = 35o, then angle EDB is equal to

1. 100°
2. 115°
3. 120°
4. 125°

9. In a right-angled triangle ABC, angle ABC = 90°, AB = 5 cm and BC = 12 cm. The radius of the circum circle of the triangle ABC is

1. 6.5 cm
2. 7 cm
3. 7.5 cm
4. 6 cm

10. If the circum radius of an equilateral triangle ABC be 8 cm, then the height of the triangle is

1. 8 cm
2. 12 cm
3. 16 cm
4. 6 cm

11. 360 sq. cm and 250 sq. cm are the areas of two similar triangles. If the length of one of the sides of the first triangle be 8 cm, then the length of the correspoding side of the second triangle is

1. 6 cm
2. 6 1/5 cm
3. 6 1/3 cm
4. 6 2/3 cm

12. If the perimeters of an equilateral triangle and that of a square are equal, then the ratio of their areas will be

1. 4 : 3
2. 4 : √3
3. 4 : 3√3
4. 4 : 2√3

13. Length of each equal side of an isosceles triangle is 10 cm and the included angle between those two sides is 45o. Find the area of the triangle.

1. 25√2 cm2
2. 35√2 cm2
3. 5√2 cm2
4. 15√2 cm2

14. In a triangle ABC, the base BC is trisected at D and E. The line through D, parallel to AB, meets AC at F and the line through E parallel to AC meets AB at G. Let EG and DF intersect at H. What is the ratio of the sum of the area of parallelogram AGHF and the area of the triangle DHE to the area of the triangle ABC?

1. 1 : 2
2. 1 : 3
3. 1 : 4
4. 1 : 6

15. PQR is an equilateral triangle. O is the point of intersection of altitudes PL, QM and RN. If OP = 8 cm, then what is the perimeter of the triangle PQR?

1. 8√3 cm
2. 12√3 cm
3. 16√3 cm
4. 24√3 cm

16. ABC is a triangle. The bisectors of the internal angle B and external angle C intersect at D. If angle BDC = 50o, then angle A is

1. 100o
2. 90o
3. 120o
4. 60o

17. If the altitude of an equilateral triangle is 12√3 cm, then its area would be:

1. 12 cm2
2. 72 cm2
3. 36√3 cm2
4. 144√3 cm2

18. If the area of an equilateral triangle is 9√3 sq cm, then what would be its altitude?

1. 6 cm
2. 6√3 cm
3. 3√3 cm
4. 9√3 cm

19. What is the ratio of areas of two similar triangles if the sides are in the ratio 5:7?

1. 5 : 7
2. 10 : 14
3. 25 : 49
4. 125 : 343

20. A triangle has 3 sides of length 5 cm, 12 cm and 13 cm. What would be the length of the median from the hypotenuse to its opposite vertex?

1. 6.5 cm
2. 6 cm
3. 7 cm
4. 5.5 cm