Practice Questions for Geometry - Triangles

1. PE 1 - Triangles | Geometry - Triangles

Two poles, of height 4 m and 6 m, are 15 m apart. The height of the point of intersection of the lines joining the top of each pole to the foot of the opposite pole is:

(a)
2.4 m
(b)
2.0 m
(c)
10.0 m
(d)
6.0 m
(e)
None of these

2. PE 1 - Triangles | Geometry - Triangles

PQRS is a trapezium in which the length of the parallel sides PQ and RS is in the ratio 3 : 4. If the diagonals intersect at O, then find the ratio of area of ΔPOQ to ΔROS.

(a)
16 : 9
(b)
9 : 16
(c)
3 : 4
(d)
None of these

3. PE 1 - Triangles | Geometry - Triangles

Consider the triangle PQR as shown in the following figure where QR = 8 cm, QS = 6 cm, SR = 4 cm and ∠SPR = ∠SRQ. What is the ratio of the perimeter of ΔPSR to that of the ΔQSR?

(a)
7/9
(b)
8/9
(c)
6/9
(d)
5/9

4. PE 1 - Triangles | Geometry - Triangles

In the given figures, angles B, C and E are all right angles. AB and BC are sides with integral length. If the length of side AC is 17 cm then find the possible value of the ratio of areas of triangle ABC and triangle BCD.

(a)
225 : 64
(b)
64 : 225
(c)
Both (a) and (b)
(d)
Cannot be determined

5. PE 1 - Triangles | Geometry - Triangles

ABC is a right angled triangle with AB = 21 units and BC = 28 units. If PQRB is a square, find its area?

(a)
81
(b)
256
(c)
144
(d)
169

6. PE 1 - Triangles | Geometry - Triangles

ABC is a right angled triangle with AB = 15 unit and BC = 20 unit. If AM = 4 unit and CO = 6 unit, find the length of LN?

(a)
12.5
(b)
17.8
(c)
21.6
(d)
19.4

7. PE 1 - Triangles | Geometry - Triangles

ABCD is a square of side 10 units. P, Q, R and S are midpoints of sides AD, DC, CB and BA respectively. Find the length of JK?

(a)
5
(b)
2√5
(c)
√10
(d)
None of these

8. PE 1 - Triangles | Geometry - Triangles

If the length of the sides of a triangle are in the ratio 5 : 12 : 13, find the ratio of the length of the altitudes of the respective sides.

(a)
5 : 12 : 13
(b)
13 : 12 : 5
(c)
156 : 65 : 60
(d)
Cannot be determined

9. PE 1 - Triangles | Geometry - Triangles

How many differently shaped triangles exist in which no two sides are of the same length, each side is of integral unit length and the perimeter of the triangle is less than 14 units?

(a)
3
(b)
4
(c)
5
(d)
6
(e)
None of these

10. PE 1 - Triangles | Geometry - Triangles

The area of a triangle with side length a, b and c (a ≥ b ≥ c) is 1 unit. Then b cannot be less than

(a)
2√2
(b)
2
(c)
√3
(d)
√2

PE 1 - Triangles | Geometry - Triangles

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