Question

Find the length of a diagonal of a square whose perimeter is 48

Answer 1

12 sq. rt. 2

Explanation:

If the perimeter is 48, then all the sides are each 12. Use the pythagorean theorem to find the diagonal, or hypotenuse

Answer 2

`\large\boxed{12\sqrt2}`

Explanation:

a - side of square

The formula of a perimeter of a square:

`P=4a`

We have P = 48. Substitute:

`48=4a` divide both sides by 4

`12=a\to a=12`

You can use the Pythagorean theorem, and calculate the length of a diagonal or use the formula of a diagonal of a square:

`d=a\sqrt2`

Substitute:

`d=12\sqrt2`