The height of a triangle is four more than twice it's base. If it's area is 24, find the height and the base.

The height is 12, and the base is 4.

Step-by-step explanation:

Let b = base

Then the height = 2b + 4

A = bh/2

bh/2 = A

b (2b + 4) / 2 = 24

2b^2 + 4b = 48

b^2 + 2b - 24 = 0

(b - 6) (b + 4) = 0

b - 6 = 0 or b + 4 = 0

b = 6 or b = 4

A base length cannot be a negative number, so we discard the solution b = 4.

b = 4

h = 2b + 4 = 2 (4) + 4 = 8 + 4 = 12

The height is 12, and the base is 4.