Question
The hypotenuse of a right triangle is 13 cm long. The longer leg is 7cm longer that the shorter leg. Find the side lengths of the triangle
Answers
GPT 3.5
Let the shorter leg be x cm long.
Then, the longer leg is x + 7 cm long.
Using the Pythagorean theorem, we have:
x^2 + (x + 7)^2 = 13^2
x^2 + x^2 + 14x + 49 = 169
2x^2 + 14x - 120 = 0
x^2 + 7x - 60 = 0
(x + 12)(x - 5) = 0
x = 5 (since side lengths of a triangle cannot be negative)
Therefore, the shorter leg is 5 cm long and the longer leg is 12 cm long.
Then, the longer leg is x + 7 cm long.
Using the Pythagorean theorem, we have:
x^2 + (x + 7)^2 = 13^2
x^2 + x^2 + 14x + 49 = 169
2x^2 + 14x - 120 = 0
x^2 + 7x - 60 = 0
(x + 12)(x - 5) = 0
x = 5 (since side lengths of a triangle cannot be negative)
Therefore, the shorter leg is 5 cm long and the longer leg is 12 cm long.