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a triangular lot in a park has a base with a measure that is 4 more than twice the height of the lot. the area of the lot is 99 square feet. since the area of a triangle is found by using the formula a=1/2 bh, the area for this lot can be represented by the equation 99=1/2(2h+4)h, where h represents the height of the triangle.
what is the height of the lot?

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!

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