Question

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.

Answer 1

If I did the math right, it should be D) 12 m

Answer 2

The area for a triangle is $A= \frac{1}{2}bh$.  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 $48= \frac{1}{2} b(b-4)$.  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 $96=b^2-4b$.  In order to solve for b, we have to factor.  Bring the 96 over to the other side by subtraction to get $b^2-4b-96=0$.  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.