In a right-angled triangle, the leg ratio is 3: 4, and its hypotenuse is 35 cm. Find the perimeter of the triangle.

univerkov | September 5, 2021 | education

Let us denote legs AB and BC by 3x and 4x, respectively, where x is unknown. Let’s use the Pythagorean theorem:

AB² + BC² = AC²;

(3x) ² + (4x) ² = 35²;

9x² + 16x² = 1225;

25x² = 1225;

x² = 1225/25 = 49;

x = √49 = 7.

So the perimeter is

P = AB + BC + AC = 3 ⋅ 7 + 4 ⋅ 7 + 35 = 84 (cm²).

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