In a right-angled triangle ABC, the angle C is straight, AB = 26, the legs are in the ratio of 5: 12. Find the large leg.

univerkov | March 13, 2021 | education

Let the length of the smaller leg BC be 5 * X cm, then, by condition, the length of the larger leg is 12 * X cm.

Let’s use the Pythagorean theorem.

AB ^ 2 = AC ^ 2 + BC ^ 2.

26 ^ 2 = (12 * X) ^ 2 + (5 * X) ^ 2.

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

169 * X ^ 2 = 676.

X ^ 2 = 676/169 = 4.

X = 2.

Then AC = 12 * 2 = 24 cm.

Answer: The length of the larger leg is 24 cm. (4).

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