Question

John is planning on building a shelf in the shape of a right triangle. He wants the shelf to be 99 inches at its widest and 4040 inches long. He believes the diagonal will be 41 inches. Is he accurate?

Answer 1

Given:

Shape of the shelf is a right triangle.

Width of the shelf = 9 inches

Length of the shelf = 40 inches

He believes the diagonal will be 41 inches.

To find:

Whether he is accurate or not.

Solution:

According to the Pythagoras theorem,

`Hypotenuse^2=Perpendicular^2+Base^2`

Using Pythagoras theorem, find the length of the diagonal.

`Diagonal^2=Width^2+length^2`

`Diagonal^2=(9)^2+(40)^2`

`Diagonal^2=81+1600`

`Diagonal^2=1681`

Taking square root on both sides.

`Diagonal=\pm √(1681)`

But side cannot be negative.

`Diagonal=41`

Therefore, the length of the diagonal is 41 inches. So, John is accurate.