Given a right-angled triangle, the leg difference is 28 meters, and the hypotenuse is 10 meters. Find the legs.

Pythagorean theorem: in a right-angled triangle, the sum of the squares of the legs is equal to the square of the hypotenuse. Let’s solve the problem using the equation, where:

x is the first leg;

(28 – x) – the second leg.

Let’s make the equation:

x² + (28 – x) ² = 10²;

x² + (28² – 2 * 28 * x + x²) = 100;

x² + 784 – 56x + x² = 100;

2x² – 56x + 684 = 0;

x² – 28x + 342 = 0;

Find the discriminant of the quadratic equation:

D = b² – 4ac = (-28) ² – 4 * 1 * 342 = 784 – 1368 = – 584

Since the discriminant is less than zero, the equation has no real solutions.