SOLUTION: A triangle has an area of 24 square meters. The base is two meters longer than the height. What is the length of the base of the triangle?

Question 797556: A triangle has an area of 24 square meters. The base is two meters longer than the height. What is the length of the base of the triangle?

Answer by waynest(281) (Show Source): You can put this solution on YOUR website!
base = h + 2
height = h
A = 1/2bh
(1/2)h(h + 2) = 24
(1/2)(h^2 + 2h) = 24
2(1/2)(h^2 + 2h) = 2(24)
h^2 + 2h = 48
h^2 + 2h - 48 = 48 - 48
h^2 + 2h - 48 = 0
factor:
(h + 8)(h - 6) = 0
h + 8 = 0
h + 8 - 8 = -8
h = -8
h - 6 = 0
h - 6 + 6 = 6
h = 6
you can not have a negative value so h = 6
check:
(1/2)(6(6 + 2)) = 24
(1/2)(6(8)) = 24
(1/2)48 = 24
24 = 24

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