Simplify the equation they gave you: 99 = 1/2*(2h + 4)*h; first multiply
99 = (h + 2)*h
99 = h² + 2h; subtract h² + 2h from both sides
99 - h² - 2h = 0; rearrange
-h² - 2h + 99 = 0; factor
(-h + 9)(h + 11) = 0; set each factor equal to 0
-h + 9 = 0 → h = 9 h + 11 = 0 → h = -11
The value of h has to be positive so lets go with 9. Plug it ito the equation to make sure.
99 = 1/2*(2(9) + 4)*9
99 = 1/2*22*9
99 = 99; that means that the answer was right → 9 is the height
I hope this helps you!
