The diagonal of the rectangle is 34, find their sides if their length is 15k8.

univerkov | September 13, 2021 | education

Let the length of the side AB = 8 * X, then the Side AD, by condition is equal to 15 * X.

From a right-angled triangle ABD, by the Pythagorean theorem,

BD ^ 2 = AB ^ 2 + AD ^ 2.

342 = (8 * X) ^ 2 + (15 * X) ^ 2.

1156 = 64 * X ^ 2 + 225 * X ^ 2.

289 * X ^ 2 = 1156.

X ^ 2 = 1156/289 = 4.

X = 2.

Then AB = 8 * 2 = 16 cm, AD = 15 * 2 = 30 cm.

Answer: The sides of the rectangle are 15 cm, 30 cm.

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