Perimeter is given by the formula:
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
