The height of a triangle is 4 m less than its base. the area of the triangle is 48 m2. find the length of the base. a 7 m b 8 m c 11 m d 12 m i think the answer is 11 m

The area for a triangle is .  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 .  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 .  In order to solve for b, we have to factor.  Bring the 96 over to the other side by subtraction to get .  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.