finding the length of two triangle sides

Question

In a right triangle, one leg is 4 ft shorter than the other leg. The hypotenuse is 12 ft Approximate the lengths of the legs to the nearest tenth of a foot.

Short leg is how long?

Long leg is how long?

Need help figuring this out! thank you!

Answer 1

Let the long leg be represented by x.

Then the short leg is represented by x-4 (4 feet less than the long leg).

Apply the Pythagorean Theorem:

(x-4)²+x²=12²

x²-8x+16+x²=144

2x²-8x-128=0

x²-4x-64=0 (might as well divide every term by 2 to make the numbers smaller)

Now use the quadratic formula to find the roots. But reject a negative root because in the context of the problem the side of a triangle must be positive. You will want to use a calculator to get the approximate answer to the nearest tenth.

desmos.com/calculator/8uidotyyni

Specifically check out rows 6 and 8 in the above graph. You can visit the URL by selecting, right-clicking, and choosing "Go to..." from the drop-down menu.

Remember the problem asks for the lengths of both legs, so subtract 4 from the value of x to get x-4.