# In a right-angled triangle, one leg is three inches shorter than the other

**In a right-angled triangle, one leg is three inches shorter than the other, and the hypotenuse is equal to 15 find the perimeter of the triangle.**

Let the length of the smaller leg be X cm, BC = X dm, then, by condition, the length of the larger leg is (X + 3) dm, AB = (X + 3) dm.

By the Pythagorean theorem, AC ^ 2 = AB ^ 2 + BC ^ 2.

152 = X ^ 2 + (X + 3 ^) 2.

225 = X ^ 2 + X ^ 2 + 6 * X + 9.

2 * X ^ 2 + 6 * X – 216 = 0.

2 + 3 * X – 108 = 0.

Let’s solve the quadratic equation.

D = b ^ 2 – 4 * a * c = 3 ^ 2 – 4 * 1 * (-108) = 9 + 432 = 441.

X1 = (-3 – √441) / (2 * 1) = (-3 – 21) / 2 = -24 / 2 = -12. (does not match, since <0).

X2 = (-3 + √441) / (2 * 1) = (-3 + 21) / 2 = 18/2 = 9.

BC = 9 dm, then AB = (9 + 3) = 12 dm.

Ravs = AB + BC + AC = 12 + 9 + 15 = 36 cm.

Answer: The perimeter of the triangle is 36 cm.