One of the legs of a right-angled triangle is 12 cm, and the length of the hypotenuse is 8 cm longer

One of the legs of a right-angled triangle is 12 cm, and the length of the hypotenuse is 8 cm longer than the length of the second leg. Calculate the perimeter.

Find the unknown sides of a right-angled triangle using the equation, where:

x cm – second leg;

8x – hypotenuse (since it is eight times larger than the second leg);

The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the legs. Let’s compose and solve the equation:

x² + 12² = 8x²;

x² + 144 = 8x²;

144 = 8x² – х²;

7x² = 144;

x² = 144/7;

x = √144 / 7 – second leg:

8x = 8 * √144 / 7 = √9216 / 7.

Find the perimeter of the triangle by adding all its sides:

P = 12 + √144 / 7 + √9216 / 7 = 12 + √20 4/7 + √1316 4/7 = 12 + √20 4/7 + 36√20 4/7 = 12 + 37√20 4 / 7 cm