A 5.5m long ladder is leaned against a wall. The ladder reaches the wall to a height of 4.4m. Find the distance between the wall and the foot of the ladder.

Solution:

Given, the length of the ladder is 5.5 m.

The ladder rests against a vertical wall.

The ladder reaches the wall to a height of 4.4m.

We have to find the distance between the wall and the foot of the ladder.

Let RQ be length of the ladder such that RQ = 5.5 m

Let PQ be the distance between the foot of the ladder and the wall.

Let RP be the height of the wall such that RP = 4.4 m

Now, RPQ is a triangle right angled at P.

By Pythagorean theorem,

RQ² = RP² + PQ²

(5.5)² = (4.4)² + PQ²

30.25 = 19.36 + PQ²

PQ² = 30.25 - 19.36

PQ² = 10.89

Taking square root,

PQ = √10.89

By using long division,

√10.89 = 3.3

Therefore, the distance between the foot of the ladder and the wall is 3.3 m.

✦ Try This: A 8 m long ladder is leaned against a wall. The ladder reaches the wall to a height of 15 m. Find the distance between the wall and the foot of the ladder.

☛ Also Check: NCERT Solutions for Class 8 Maths

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NCERT Exemplar Class 8 Maths Chapter 3 Problem 128

A 5.5m long ladder is leaned against a wall. The ladder reaches the wall to a height of 4.4m. Find the distance between the wall and the foot of the ladder

Summary:

A 5.5m long ladder is leaned against a wall. The ladder reaches the wall to a height of 4.4m. The distance between the wall and the foot of the ladder is 3.3 m.

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