Question

Find the length of the diagonal of a square with perimeter of 24

Answer 1

d = 6sqrt(2) or 8.4853

Explanation:

Formula

P = 4*s

s^2 + s^2 = d^2 where d is the diagonal and s is the side.

Givens

P = 24

Solution

P = 4s Substitute for s

24 = 4*s Divide by 4

24/4 = s

s = 6

================

d^2 = s^2 + s^2

d^2 = 6^2 + 6^2

d^2 = 36 + 26

d^2 = 72

d = sqrt(72)

Factors of 72

72: 6 * 6 * 2

Rule: Every pair of = factors allows you to take one of them outside the sqrt sign and throw the other a way. If there are no pairs, whatever you started with stays under the root sign.

sqrt(6*6*2) = 6sqrt(2)

• The diagonal length is either
• d = 6*sqrt(2) or
• d = 8.4853