One of the legs of a right-angled triangle is 3 cm larger than the other. Find the perimeter

One of the legs of a right-angled triangle is 3 cm larger than the other. Find the perimeter of the triangle if its hypotenuse is 15 cm.

1) Let x cm be the length of one of the legs of the triangle.

2) Then (x + 3) cm is the length of the other leg.

3) According to the Pythagorean theorem in a right-angled triangle, the sum of the squares of the legs is equal to the square of the hypotenuse. Therefore, we can write:

x ^ 2 + (x + 3) ^ 2 = 15 ^ 2.

4) Let’s solve the resulting equation:

x ^ 2 + x ^ 2 + 6x + 9 = 225;

2x ^ 2 + 6x – 216 = 0;

x ^ 2 + 3x – 108 = 0.

By Vieta’s theorem, we find that x1 = 9, x2 = -12.

5) x = -12 cannot be a solution to the problem.

6) We get that x = 9 cm – the length of one leg.

7) 9 + 3 = 12 cm – the length of the other leg.

8) Calculate the perimeter of a given triangle as the sum of the lengths of its sides:

9 + 12 + 15 = 36 cm.

Answer: 36 cm.