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vladimir1956 [14]
3 years ago
10

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

Mathematics
1 answer:
julsineya [31]3 years ago
8 0

Answer:

d = 6sqrt(2) or 8.4853

Step-by-step explanation:

<u><em>Formula</em></u>

P = 4*s

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

<u><em>Givens</em></u>

P = 24

<u><em>Solution</em></u>

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

<em><u>Rule</u></em>: 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

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