Question

The length of the longer leg of a right triangle is 19 cm more than five times the length of the shorter leg. The length of the hypotenuse is 20 cm more than five times the length of the shorter leg. Find the side lengths of the triangle

Answer 1

13 cm, 84 cm, 85 cm

Explanation:

Let the sides of triangle are be a, b, c

• a = x, b = 5x + 19, c = 5x + 20

As per Pythagorean theorem:

• c² = a² + b²
• (5x+20)² = (5x +19)² + x²
• 25x² + 200x + 400 = 25x² + 190x + 361 + x²
• x² - 10x - 39 = 0

Solving the quadratic equation we get:

• x= 13

Then:

• a= 13 cm
• b = 5*13 +19 = 84 cm
• c= 5*13 + 20 = 85 cm