The hypotenuse of a right-angled triangle is 10 cm, and one of the legs is 2 cm larger than the other.

The hypotenuse of a right-angled triangle is 10 cm, and one of the legs is 2 cm larger than the other. Find the legs of the triangle?

Let x be the first leg
x + 2 – second leg
By the Pythagorean theorem
10² = (x + 2) ² + x²
2x² + 4x- 96 = 0 (divided by 2)
x² + 2x – 48 = 0
D = 2²-4 * (- 48) = 196
√D = 14
x1 = (- 2 + 14) / 2 = 6
x2 <0 – exclude, because leg cannot be negative
x + 2 = 6 + 2 = 8
Answer: 6 cm and 8 cm