In rectangle ABCD, the adjacent sides are 12: 5, and its diagonal is 26. What is the smaller side of the rectangle?

univerkov | May 5, 2021 | education

Let the length of the smaller side of the rectangle be 5 * X cm, AB = 5 * X cm, then, by condition, the length of the larger side is 12 * X cm, BC = 12 * X cm.

Then in a right-angled triangle ABC, by the Pythagorean theorem, AB ^ 2 + BC ^ 2 = AC ^ 2.

25 * X ^ 2 + 144 * X ^ 2 = 676.

169 * X ^ 2 = 676.

X ^ 2 = 676/169 = 4.

X = 2.

Then AB = CD = 2 * 5 = 10 cm.

Answer: The smaller side of the rectangle is 10 cm.

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