The area of a right-angled triangle is 30 cm2 and the sum of the legs is 17 cm, find the hypotenuse of the triangle.

1. Vertices of the triangle – А, В, С. А = 90 °.

2. We take the length of the leg AB for x, the length of the leg AC for y.

3. Let’s compose two equations:

x x y / 2 = 30; x x y = 60; x = 60 / y:

x + y = 17;

4. Substitute x = 60 / y into the second equation:

60 / y + y = 17;

y² – 17y + 60 = 0.

The equation has two roots.

The first value of y = (17 + √289 – 240) / 2 = (17 + 7) / 2 = 12;

The second value is y = (17 – 7) / 2 = 5.

Each of the legs has two meanings:

AB = 12 cm and 5 cm.

AC = 5 cm and 12 cm.

5. Hypotenuse BC = √144 + 25 = 13 cm.