A right triangle has an area of x^2-4 One leg has a length of 2 x+4. What is the ratio of the area of the triangle to the leg.

Answer 1

Since the expression x^2 -4 is the difference of two squares, it can be factored into the following terms:

(x-2)(x+2)

The expression 2x + 4 can be factored as:

2(x+2)

The ratio of the area to the leg would then be:

(x-2)(x+2)/ 2(x+2)

Then (x+2)/((x+2) is equivalent to one (or they cancel out), so the expression becomes:

(x-2)/2

So the ratio of the area to the leg is (x-2) / 2