Question

How do you find diagonal of a square with a side length of 6?

Answer 1

6√2 ≈ 8.49

Explanation:

They are two ways:

METHOD 1:

Use the Pythagorean theorem:

`leg^2+leg^2=hypotenuse^2`

On the square, the legs are the sides of the square, and the hypotenuse is the diagonal of the square.

We have two the same legs = 6.

Let d - diagonal

Substitute:

`6^2+6^2=d^2\\\\d^2=36+36\\\\d^2=(36)(2)\to d=√((36)(2))\\\\d=√(36)\cdot\sqrt2\\\\d=6\sqrt2`

METHOD 2:

Use the formula of a diagonal of a square:

`d=s\sqrt2`

d - diagonal

s - side

We have s = 6.

Substiute:

`d=6\sqrt2`