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What is the maximum area of a triangle having 15 cm as the sum of its base and height?
Wiki User
∙ 11y ago
Let b = x, so h = 15 - x.
A = (bh)/2
A(x) = [x(15 - x)]/2
A(x) = -(1/2)x2 + (15/2)x
since the coefficient of x2 is negative, we have a maximum value of the area when x = (-15/2)/[2(-1/2) = 15/2
A(15/2) = -(1/2)(15/2)2 + (15/2)(15/2)] = -225/8 + 225/4 = (-225 + 500)/8 = 225/8
Thus, the maximum area of the given triangle would be 225/8 cm2.
Wiki User
∙ 11y ago
Budd
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