The hypotenuse of a right-angled triangle is 39 cm. It is known that one leg is 21 cm larger than the other.

The hypotenuse of a right-angled triangle is 39 cm. It is known that one leg is 21 cm larger than the other. Find the perimeter of this triangle.

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

2. Let’s designate the leg AB with the symbol “a”.

3. Let’s make an equation, taking into account that the AC leg is 21 centimeters larger than the AB leg:

(a + 21) ² + a² = 39²;

a² + 42a + 441 + a² = 1521;

2а² + 42а – 1080 = 0;

a² + 21a – 540 = 0;

The first value a = (- 21 + √441 + 2160) / 2 = (- 21 + 51) / 2 = 15;

The second value a = (- 21 – 51) / 2 = – 36 – does not satisfy the condition of the problem.

AB = 15 centimeters.

AC = 15 + 21 = 36 centimeters.

P = 15 + 36 + 39 = 90 centimeters.