High School

The long leg of a right triangle is 97 feet longer than the short leg. The hypotenuse is 113 feet long. How long are the legs of the right triangle?

a) Short leg: 8 feet, Long leg: 105 feet
b) Short leg: 56 feet, Long leg: 153 feet
c) Short leg: 45 feet, Long leg: 142 feet
d) Short leg: 57 feet, Long leg: 154 feet

Answer :

Final answer:

The correct lengths of the legs of the right triangle, using the Pythagorean theorem, are 56 feet for the short leg and 153 feet for the long leg.

Explanation:

This problem can be solved using the Pythagorean theorem, which states that in a right-angled triangle the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. If we denote the length of the short leg as x (in feet), then the length of the long leg is x + 97 feet. The Pythagorean theorem then gives us the equation:

x² + (x + 97)² = 113²

Solving this quadratic equation for x, we find that x is approximately 56 feet, which means the short leg of the triangle is 56 feet long and the long leg is 56 + 97 = 153 feet long. Therefore, the correct answer is (b) Short leg: 56 feet, Long leg: 153 feet.

Learn more about Pythagorean theorem here:

https://brainly.com/question/19649203

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