Question

The second-story gutters are twenty-four feet from the ground and need repair. If a ladder is placed ten feet from the base of the house and it reaches the gutters, how long is the ladder?

Answer 1

The length of the ladder is 26 feet.

Solution:

Given, The second-story gutters are twenty-four feet from the ground and need repair.

A ladder is placed ten feet from the base of the house and it reaches the gutters,

We have to find how long is the ladder?

We can observe that, ladder ground and building forms a right angle triangle.

Ladder is hypotenuse side and remaining are legs of right angle triangle.

Pythagorean theorem states thatt square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

Hence we get,

`\begin{array}{l}{\rightarrow \text { hypotenuse }^(2)=10^(2)+24^(2)} \\\\ {\rightarrow \text { hypotenuse }^(2)=100+576} \\\\ {\rightarrow \text { hypotenuse }=√(676)=26}\end{array}`

Hence, the length of the ladder is 26 feet.