# One of the legs of a right-angled triangle is 9 cm less than the hypotenuse, and the other is 7 cm

**One of the legs of a right-angled triangle is 9 cm less than the hypotenuse, and the other is 7 cm larger than the first. Find the hypotenuse if the area of the triangle is 60 cm2.**

Let us denote the hypotenuse by the letter x. Then the first leg is (x – 9) cm. The second leg is 7 cm larger than the first: x – 9 + 7 = x – 2 (cm).

The area of a rectangular triplet is equal to half of the product of legs and is equal to 60 cm², we make the equation: (x – 2) (x – 9) / 2 = 60.

We solve the equation:

x² – 2x – 9x + 18 = 120.

x² – 11x + 18 – 120 = 0.

x² – 11x – 102 = 0.

We solve the quadratic equation through the discriminant.

D = 121 + 408 = 529 (√D = 23);

x1 = (11 – 23) / 2 = -12/2 = -6 (not suitable).

x2 = (11 + 23) / 2 = 17 (cm).

Answer: 2) the hypotenuse of the triangle is 17 cm.