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## Answers

P = 2L + 2W

and in this case you have 34 as the perimeter then you'll have:

34 = 2L + 2W ----equation 1

given that the diagonal is 13 and using pythagorean theorem you'll have:

13² = L² + W² ---equation 2

dividing equation 1 by 2 and rearranging you'll have:

34 = 2L + 2W

17 = L + W

L = 17 -W ----equation 3

substitute equation 3 to equation 2

13² = L² + W²

13² = (17 - W)² + W²

13² = 17² - 34W + W² + W²

2W² - 34W + 17² - 13² = 0

2W² - 34W +120 = 0

dividing the whole equation by 2

W² - 17W + 60 = 0

(W - 12) (W - 5) = 0

W = 12, W = 5

taking W=5 and substituting it to equation 3

L = 17 - W

L = 17 - 5

L =12

(why i chose 5? simply because we have that idea that in most cases, the length is longer than the width)

Area of the rectangle then is

A = LW

A = 12(5)

__A = 60 square units__