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

The area of a right-angled triangle is calculated by the formula: S = a * b / 2
we get:
15 = ab / 2 = ab = 30
let’s make a system:
ab = 30
a + b = 11

ab = 30
a = 11 – b

(11 – b) * b = 30 (*)
a = 11 – b

* 11b – b ^ 2 – 30 = 0
D = 121 – 120 = 1
b = -11 + – 1 / – 2 = 5; 6

If we substitute these numbers under a, then we get the same answers, it turns out that the legs are 5 and 6.

Answer: 5 and 6