# 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.

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.

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