The area of a right-angled triangle is 180 m ^ 2. Find the legs of this triangle if one is 31m larger than the other.

Let’s represent one of the legs of a right-angled triangle as x. Then the second leg will be x + 31 m.And their product will be equal to the area of a right-angled triangle multiplied by 2.

Let’s compose and solve the equation.

x * (x + 31) = 180 * 2.

x² + 31 * x = 360.

x² + 31 * x – 360 = 0.

D = 961 + 1440 = 2401.

x1 = (-31 + √2401) ÷ 2 = 9.

x1 = (-31 – √2401) ÷ 2 = -40.

Answer: the legs of a right-angled triangle are 9 m and 40 m.