The lengths of the legs of a right-angled triangle are 3: 4, and the length of the hypotenuse is 50 cm

The lengths of the legs of a right-angled triangle are 3: 4, and the length of the hypotenuse is 50 cm. Find the area of the triangle.

We find the legs of the triangle according to the Pythagorean theorem (the sum of the squares of the legs is equal to the square of the hypotenuse) using the equation, where:

3x – smaller leg;

4x – larger leg;

Let’s compose and solve the equation:

(3x) ² + (4x) ² = 50²;

9x² + 16x² = 2500;

25x² = 2500;

x² = 100;

x = √100;

x = 10;

3x = 3 * 10 = 30 cm – the smaller leg of the triangle;

4x = 4 * 10 = 40 cm – the larger leg of the triangle.

The area of a right-angled triangle is equal to the half-product of the legs;

S = 1/2 * 40 * 30 = 20 * 30 = 600 cm².

Answer: 600 cm²