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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

Solution:

Given, the length of the ladder is 10 m

The foot of the ladder leaning against a vertical wall is 6 m away from the base of the wall.

We have to find the point on the wall where the top of the ladder reaches.

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

In the figure,

PR is the ladder = 10 m

RQ is the distance from the base of the wall to the foot of the ladder = 6 m

PQ is the height of the point on the wall where the top of the ladder reaches.

By using Pythagorean theorem,

PR² = PQ² + RQ²

(10)² = PQ² + (6)²

100 = PQ² + 36

PQ² = 100 - 36

PQ² = 64

Taking square root,

PQ = 8 m

Therefore, the height of the point on the wall where the top of the ladder reaches is 8 m.

✦ Try This: Foot of a 15 m long ladder leaning against a vertical wall is 8 m away from the base of the wall. Find the height of the point on the wall where the top of the ladder reaches

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6

NCERT Exemplar Class 10 Maths Exercise 6.3 Problem 15

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

Summary:

Foot of a 10 m long ladder leaning against a vertical wall is 6 m away from the base of the wall. The height of the point on the wall where the top of the ladder reaches is 8 m

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