The area for a triangle is [tex]A= \frac{1}{2}bh [/tex]. We have an expression that puts the height in terms of the base. We are told that the height is 4 m less than the base. Therefore, h = b - 4. We are also given a value for the area. So our formula is [tex]48= \frac{1}{2} b(b-4)[/tex]. To avoid the confusion of what to do with the 1/2, let's multiply both sides by 2: 96 = b(b-4). Distributing through the parenthesis, we have [tex]96=b^2-4b[/tex]. In order to solve for b, we have to factor. Bring the 96 over to the other side by subtraction to get [tex]b^2-4b-96=0[/tex]. Factor that however you are most familiar to get that your b values are 12 and -8. The two things in math that will never EVER be negative are distance/length and time. Therefore, -8 cannot be the length of our base. 12 is the answer D.
