# The perimeter of the rectangle is 82 m and the diagonal is 29 m. Find the sides.

December 26, 2020 | education

| the perimeter is the sum of the lengths of the sides. P = 2 (x + y), then x + y = P / 2 = 41

and the diagonal can be found by the Pythagorean theorem: 29 ^ 2 = x ^ 2 + y ^ 2

then we compose the system: x + y = 41; 29 ^ 2 = x ^ 2 + y ^ 2

from the first we express x and substitute: x = 41-y; 841 = (41-y) ^ 2 + y ^ 2

841 = 1681-82y + y ^ 2 + y ^ 2

2y ^ 2-82y + 840 = 0 /: 2

y ^ 2-41y + 420 = 0

D = 1681-4 * 420 = 1

y1 = (41 + 1) / 2 = 21

y2 = (41-1) / 2 = 20

Substituting into the first we get that x1 = 20, x2 = 21

But since the sides are not important to us, then the answer is 20, 21

Answer: 20 m, 21 m

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