Question

The hypotenuse of a right triangle is 7 feet long. One leg is 4 feet longer than the other. Find the lengths of the legs, Round to the nearest tenth of a foot
The length of the shorter leg is ft, and the length of the longer leg is ft.
(Do not round until the final answer. Then round to the nearest tenth as needed)
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Answer 1

Answer:

Shorter leg = 2.5 ft.

Longer leg = 6.5 ft.

Step-by-step explanation:

a^2 + b^2 = c^2

Because the hypotenuse = 7 ft, a^2 + b^2 = 49

To represent the two legs, we can use x and x+4.

x^2 + (x+4)^2 = 49

Simplifying this equation using FOIL gives us 2x^2 + 8x - 33 = 0.

Then, using the quadratic formula, we find that x = 2.5.

Thus, the shorter leg is 2.5 ft. and, when 4 is added, the longer leg is 6.5 ft.