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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