The sum of the legs of a right-angled triangle is 7cm, and the area is 6cm2. Find the hypotenuse.

1. A, B, C – the vertices of the triangle. Angle B is straight.

2. We take as x the length of the leg AB, the length of the leg AC- (7 – x).

3. Let’s compose an equation using the formula for calculating the area of a triangle:

x (7 – x) / 2 = 6;

7x – x² = 12;

x² – 7x + 12 = 0;

4. The equation has two roots:

The first value of x = (7 + √49 – 48) / 2 = 4.

The second value is x = (7 -1) / 2 = 3.

AB = 4 cm or AB = 3 cm.

AC = 7 – 4 = 3 cm or AC = 7 – 3 = 4 cm.

5. BC = √AB² + AC² = √16 + 9 = 5 cm or BC = √9 + 16 = 5 cm.

Answer: hypotenuse BC = 5 cm.