5. The length of one leg of a right triangle is 5 centimeters shorter than the hypotenuse. The hypotenuse is 15 centimeters. What is the length of the unknown leg of the right triangle rounded to the nearest tenth?

In this right triangle, we know that the hypotenuse measures 15 centimeters. According to the problem, one leg is 5 centimeters shorter than the hypotenuse, so we can find that leg's length by calculating 15 cm - 5 cm, which equals 10 cm. Now, we can let the unknown leg be represented as \( x \). Using the Pythagorean theorem: \[ x^2 + 10^2 = 15^2 \] This simplifies to: \[ x^2 + 100 = 225 \] Now, subtract 100 from both sides: \[ x^2 = 125 \] Taking the square root gives: \[ x = \sqrt{125} \approx 11.2 \text{ centimeters} \] So, the length of the unknown leg of the right triangle is approximately 11.2 centimeters.