Acity lot has the shape of a right triangle whose hypotenuse is 2 ft longer than one of the other sides. the perimeter of the lot is 364 ft. how long is each side of the lot?

Suppose that, in the triangle ABC, the hypothenuse is AC. Let's call its length [tex ] \overline{AC} = x [/tex].

The hypothenuse is 2 ft longer than one of the legs (say AB, for example). This means that

Finally, we can find the other leg with the pythagorean theorem:

So, the perimeter (i.e. the sum of the sides) is given by

Isolate the square root to get

Divide all sides by 2:

Square both sides:

This equation has solutions or . These solutions lead to, in the first case,

In the second case, you have

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step-by-step explanation: