One of the legs of the triangle is 11 cm smaller than the other, and the area is 350 cm2. What are the legs of a triangle?

Let the length of the first leg be equal to X, then the length of the second leg will be (X – 11).

The area of a right-angled triangle is half the product of its legs.

S = (a * b) / 2 = (X * (X – 11)) / 2 = 350.

X ^ 2 – 11 * X = 350.

X ^ 2 – 11 * X – 350 = 0.

Let’s solve the quadratic equation.

D = b ^ 2 – 4 * a * c = (-11) ^ 2 – 4 * 1 * (-350) = 121 + 1400 = 1521.

x1 = (11 – √1521) / (2 * 1) = (11 – 39) / 2 = -28 / 2 = -14. (Doesn’t match because <0).

x1 = (11 + √1521) / (2 * 1) = (11 + 39) / 2 = 50/2 = 25.

The first leg is 25 cm.

The second is 25 – 11 = 14 cm.

Answer: The sizes of the legs are 25 and 14 cm.