Question

A square has an area of 44.89in^2. How do you get the length of the diagonal of the square?

Answer 1

Find the length of a side by taking the square root of the area:

Side = sqrt44.89 = 6.7 inches.

Now to find the length of the diagonal multiply the side length by the sqrt of2:

Diagonal = 6.7Sqrt(2) ( exact length)

As a decimal= 9.4752

Answer 2

`6.7√(2)\ in`

Explanation:

Let x inches be the length of the side of the square. The area of the square is

`x\cdot x=x^2\ in^2`

Then

`x^2=44.89\\ \\x=6.7\ in`

By the Pythagorean theorem,

`d^2=6.7^2+6.7^2\\ \\d^2=44.89+44.89\\ \\d^2=89.78\\ \\d=√(89.78)=6.7√(2)\ in`