The area of a right-angled triangle is 15 dm2, and the sum of its legs is 11 dm. Find legs.

Suppose one of the legs is equal to x dm. Since the sum of the two legs is 11 dm, the second leg will be (11 – x) dm. The area of a right-angled triangle will be equal to the half-product of the legs, that is, x * (11 – x) / 2, which is equal to 15 sq. dm. We got the equation:

x * (11 – x) / 2 = 15;

x * (11 – x) = 15 * 2;

– x * x + 11 * x = 30;

x * x – 11 * x + 30 = 0.

Hence, by Vieta’s theorem, we find that x = 5 or x = 6.

Then the legs will be 5 dm and 6 dm or 6 dm or 5 dm.