Question

The area of a square is 72 square feet. What is the length of a diagonal of the square?

Answer 1

Our keys for this problem is the pythagorean theorem and the are formula `A=l^2` where `l` is the length of the vertices.

Explanation:

So the lenght of the vertices is `l=sqrt(A)=sqrt(72)`feet
If you consider the orthogonal traingle composed of two vertices and the diagonal of the square then the diagonal is the hypotenuse.
So the lenght of it is `L=sqrt(sqrt(72)^2+sqrt(72)^2)=sqrt(2*72)`
`sqrt(144)=12`feet

Answer 2

See explanation.

Explanation:

First we find the side length:

`A=a^2`

`a=sqrt(A)=sqrt(72)=6sqrt(2)`

Now we can calculate the diagonal:

`d=asqrt(2)=6sqrt(2)sqrt(2)=12`

Answer:

The diagonal is 12 feet long.