Question

What is the lenght of a diagonal of a square with sides 16feet

long ? Round to the nearest tenth.

Answer 1

The length of the diagonal is 22.6 ft.

Explanation:

To find the length of the diagonal of a square, multiply the length of one side by the square root of 2:

If the length of one side is x,
`length = x√(2)` as you can see in the image attached.

This fact is a consequence of applying the Pythagoras' Theorem to find the length of the diagonal if we know the side length of the square.

`length^(2)  = x^(2)+x^(2)  \\ length=\sqrt{x^(2)+x^(2)} \\ length=\sqrt{2x^(2) } \\ length=x√(2)`

We know that the length of one side is 16 ft so
`length = 16√(2)=22.627` and round to the nearest tenth is 22.6 ft