Question

A right triangle has one leg three times the length of the other and a perimeter of 30. Find the exact lengths of the three sides.

Answer 1

The lengths of the sides of a right triangle with one leg three times longer than the other and a perimeter of 30 are 3, 9, and 18.

Step-by-step explanation:

To solve for the lengths of the sides of a right triangle where one leg is three times longer than the other, and the perimeter is 30, we start by letting the shorter leg be x, the longer leg be 3x, and the hypotenuse be c. Using the given information, the perimeter P can be written as:

P = x + 3x + c = 30

We know from the Pythagorean theorem that a² + b² = c². In our case, we have x and 3x as the legs, so:

x² + (3x)² = c² which simplifies to x² + 9x² = c² or 10x² = c².

Combining our equations, we have two equations with two unknowns:

• 4x + c = 30
• 10x² = c²

Solving this system of equations, we find that:

• x = 3
• c = 18

Thus, the lengths of the sides are 3, 9, and 18.