# NCERT Mathematics Class 10 Exemplar Ch 6 Triangles Part 6

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**EXERCISE 6.4**

1. In Fig. 6.16, if , , , and , then find the lengths of PD and CD.

Answer:

2. It is given that such that , , and . Find the lengths of the remaining sides of the triangles.

Answer: , .

3. Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides, then the two sides are divided in the same ratio.

4. In Fig 6.17, if PQRS is a parallelogram and , then prove that .

5. 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 find the distance by which the top of the ladder would slide upwards on the wall.

Answer:

6. For going to a city B from city A, there is a route via city C such that , and . It is proposed to construct a highway which directly connects the two cities A and B. Find how much distance will be saved in reaching city B from city A after the construction of the highway.

Answer:

7. A flag pole high casts a shadow long. Find the distance of the top of the pole from the far end of the shadow.

Answer:

8. A street light bulb is fixed on a pole 6 m above the level of the street. If a woman of height casts a shadow of 3m, find how far she is away from the base of the pole.

Answer: