Question

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

Answer 1

Answer:

The length of the diagonal is 22.6 ft.

Step-by-step 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, $length = x\sqrt{2}$ 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.

$length^{2} = x^{2}+x^{2} \\ length=\sqrt{x^{2}+x^{2}} \\ length=\sqrt{2x^{2} } \\ length=x\sqrt{2}$

We know that the length of one side is 16 ft so $length = 16\sqrt{2}=22.627$ and round to the nearest tenth is 22.6 ft