One of the legs of a right-angled triangle is 7 cm less than the other leg and 8 cm less than

One of the legs of a right-angled triangle is 7 cm less than the other leg and 8 cm less than the hypotenuse. Find the hypotenuse.

1. Let’s denote the legs and hypotenuse of a right-angled triangle a, b and c. Then, according to the condition of the problem, we can compose the equations:

b = a + 7;

c = a + 8.

2. By the Pythagorean theorem:

a ^ 2 + b ^ 2 = c ^ 2;

a ^ 2 + (a + 7) ^ 2 = (a + 8) ^ 2;

a ^ 2 + a ^ 2 + 14a + 49 = a ^ 2 + 16a + 64;

a ^ 2 + 14a – 16a + 49 – 64 = 0;

a ^ 2 – 2a – 15 = 0;

D / 4 = 1 + 15 = 16; √D = √16 = 4;

a = 1 ± 4;

a1 = 1 – 4 = -3, does not make sense;

a2 = 1 + 4 = 5 (cm);

b = a + 7 = 5 + 7 = 12 (cm);

c = a + 8 = 5 + 8 = 13 (cm).

Answer. Hypotenuse of triangle: 13 cm.