The hypotenuse of a right-angled triangle is 10 centimeters. Find his legs if their sum is 14 centimeters.

1) Let x cm be the length of one leg, then (14 – x) cm is the length of the second leg.

2) By the Pythagorean theorem, the sum of the squares of the legs is equal to the square of the hypotenuse:

x ^ 2 + (14 – x) ^ 2 = 10 ^ 2.

3) Solve the equation:

x ^ 2 + 196 – 28x + x ^ 2 = 100;

2x ^ 2 – 28x + 96 = 0;

x ^ 2 – 14x + 48 = 0.

By Vieta’s theorem:

x1 + x2 = 14;

x1 * x2 = 48, where x1 and x2 are the roots of the equation x ^ 2 – 14x + 48 = 0.

We select and get: x1 = 6, x2 = 8.

4) One leg of the triangle is either 6 cm or 8 cm.

5) Then the second leg:

14 – 6 = 8 cm

or 14 – 8 = 6 cm.

Answer: 6 and 8 cm.