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.