A ladder 10m long rests against a vertical wall. If the foot of the ladder is 6m away from the wall and the ladder just reaches the top of the wall, how high is the wall

Solution:

Given, the length of the ladder is 10 m.

The ladder rests against a vertical wall.

The foot of the ladder is 6 m away from the wall.

The ladder just reaches the top of the wall.

We have to find the height of the wall.

Let AW be the ladder such that AW = 10m 

Let AL be the distance between the foot of the ladder and the wall such that AL = 6m

Let WL be the height of the wall such that WL = x m

Now, AWL is a triangle right angled at L.

By Pythagorean theorem,

AW² = AL² + WL²

(10)² = (6)² + x²

100 = 36 + x²

x² = 100 - 36

x² = 64

Taking square root,

x = 8 m

Therefore, the height of the wall is 8 m.

✦ Try This: A ladder 12m long rests against a vertical wall. If the foot of the ladder is 8m away from the wall and the ladder just reaches the top of the wall, how high is the wall

☛ Also Check: NCERT Solutions for Class 8 Maths

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NCERT Exemplar Class 8 Maths Chapter 3 Sample Problem 28

A ladder 10m long rests against a vertical wall. If the foot of the ladder is 6m away from the wall and the ladder just reaches the top of the wall, how high is the wall

Summary:

A ladder 10m long rests against a vertical wall. If the foot of the ladder is 6m away from the wall and the ladder just reaches the top of the wall, the height of the wall is 8 m

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