Question

The shorter leg of a right triangle is 3 centimeters less than the other leg. If the hypotenuse is 15 centimeters, find the lengths of the two legs.

Answer 1

The shorter leg of the right triangle is 8 centimeters, while the other leg is 11 centimeters.

Step-by-step explanation:

Let the shorter leg of the right triangle be x, and the other leg be x+3. According to the Pythagorean theorem, the sum of the squares of the two legs is equal to the square of the hypotenuse.

So, we have the equation: x^2 + (x+3)^2 = 15^2.

By expanding and simplifying the equation, we get x^2 + x^2 + 6x + 9 = 225.

Combining like terms and solving for x, we find that x = 8.

Therefore, the lengths of the two legs are 8 centimeters and 11 centimeters.