Question

Foot of a 10 m long ladder leaning against a vertical wall is 6 m away from the base of the wall. Find the height of the point on the wall where the top of the ladder reaches.

NCERT Class X
Mathematics - Exemplar Problems

Chapter _TRIANGLES

Answer 1

By applying Pythagoras Theorem,

Height of point on the top where the ladder reaches
= square root of ( 10*10 - 6*6) m
= square root of (100-36) m
= square root of (64) m = 8 m

Answer 2

Let PR be the ladder and QR be the vertical wall.

Length of the ladder PR = 10 m

PQ = 6 m

Let height of the wall, QR = h

According to Pythagoras theorem,

PR2 = PQ2+QR2

102 = 62+QR2

100 = 36+QR2

QR2 = 100-36

QR2 = 64

Taking square root on both sides,

QR = 8

Hence the height of the wall where the top of the ladder reaches is 8 m.