The perimeter of a right-angled triangle is 60 cm. The hypotenuse is 25 cm. One leg is 5 cm less than the other.

The perimeter of a right-angled triangle is 60 cm. The hypotenuse is 25 cm. One leg is 5 cm less than the other. Find the legs of the trumpet.

The first leg is denoted by x, the second by x + 5
By the Pythagorean theorem: x ^ 2 + (x + 5) ^ 2 = 25 ^ 2 x ^ 2 + x ^ 2 + 10x + 25 = 625 2x ^ 2 + 10x – 600 = 0 | divide by 2 x ^ 2 + 5x – 300 = 0 D = 25 + 1200 = 1225 x1 = (- 5 + 35) / 2 = 15 x2 = (- 5-35) / 2 = -20 – extraneous root
One leg is x = 15, the second is x + 5 = 15 + 5 = 20
Check (find the perimeter): 15 + 20 + 25 = 60 => true
Answer: 15 and 20.