In a right-angled triangle, one of the legs is 3 cm less than the hypotenuse

In a right-angled triangle, one of the legs is 3 cm less than the hypotenuse, and the other is 6 cm less than the hypotenuse. Find the hypotenuse.

A right-angled triangle is given.

Let x be the hypotenuse.

Since one of the legs is 3 cm less than the hypotenuse, then we get x – 3.

Since the second of the legs is 6 cm less than the hypotenuse, then we get x – 6.

Find x.

Let’s make an equation.

x ^ 2 = (x – 3) ^ 2 + (x – 6) ^ 2;

x ^ 2 = x ^ 2 – 6 * x + 9 + x ^ 2 – 12 * x + 36;

x ^ 2 = 2 * x ^ 2 – 18 * x + 45;

2 * x ^ 2 – x ^ 2 – 18 * x + 45 = 0;

x ^ 2 – 18 * x + 45 = 0;

x1 = 3;

x2 = 15;

x = 3 does not fit, so the hypotenuse is 15.

Find the legs: 15 – 3 = 12 and 15 – 6 = 9.

Answer: The hypotenuse is 15.