The area of a right-angled triangle is 5 dm ^ 2 and the sum of the legs is 11 dm, find the legs.

Let’s imagine one of the legs as x, then the second will be 11 dm – x.

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

x * (11 dm – x) ÷ 2 = 5 dm².

11 dm * x – x² = 10 dm².

11 dm * x – x² – 10 dm² = 0.

Using Vieta’s theorem, we determine x1 and x2.

x1 = 1 dm, x2 = 10 dm.

Answer: the legs are equal to 1 in. And 10 in.