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.

A 7 m
B 8 m
C 11 m
D 12 m
I think the answer is 11 m

Answer 1

The area for a triangle is
`A= (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= (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.

Answer 2

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