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

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

From the very beginning, it is worth writing down the formula connecting the legs and the hypotenuse (Pythagoras’ theorem):

a ^ 2 + b ^ 2 = c ^ 2.

Let the smallest of the legs be x cm.Then, in accordance with the condition of the problem, the second leg is (x + 7) cm, and the hypotenuse is (x + 9) cm.

Let’s write the equation and solve it:

x ^ 2 + (x + 7) ^ 2 = (x + 9) ^ 2;
x ^ 2 + x ^ 2 + 14 * x + 49 = x ^ 2 + 18 * x + 81;
x ^ 2 – 4 * x – 32 = 0.

By Vieta’s theorem, we find the roots of the quadratic equation:

x1 = 8;
x2 = – 4 (not beats conv.).

Then the hypotenuse will be equal to: 8 + 9 = 17 (cm).