# One leg of a right-angled triangle is 8. The other leg is three times smaller than the hypotenuse. Find the hypotenuse.

July 28, 2021 | education

| 1. A, B, C – the vertices of the triangle. AB = 8 centimeters. ∠А = 90 °. AC is 3 times less than BC.

2. We take the length of the AC leg as x, the length of the BC hypotenuse – 3x.

3. Using the formula of the Pythagorean theorem, we compose the equation:

x² + 8² = (3x) ²;

x² +64 = 9x²;

8x² = 64;

x² = 8;

x = √8 = √4 x 2 = 2√2.

AC = 2√2 centimeters.

BC = 3 x 2√2 = 6√2 centimeters.

Answer: the length of the hypotenuse is 6√2 centimeters.

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