# The diagonals of the parallelogram are 14 and 8 cm and the perimeter is 32 cm find the sides of the parallelogram.

July 29, 2021 | education

| To solve the problem, we will use the property of the parallelogram diagonals, which is as follows: the sum of the squares of the sides of the parallelogram will be equal to the sum of the squares of its diagonals. And the formula for finding the perimeter of a parallelogram. We get the system, taking into account that the lengths of the sides are x cm and y cm.

2 * (x + y) = 32 and 2 * (x ^ 2 + y ^ 2) = 14 ^ 2 + 8 ^ 2.

After simplification:

x + y = 16, whence y = 16 – x.

x ^ 2 + y ^ 2 = 130;

x ^ 2 + (16 – x) ^ 2 = 130;

2 * x ^ 2 – 32 * x + 126 = 0;

x ^ 2 – 16 * x + 63 = 0.

x = 7 or x = 9.

y = 9 or y = 7.

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