SOLUTION: A triangle has a height of 2x and a base of 7 - 4x. a) what is the maximum area of the triangle? b) what value of x gives the maximum area?

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Question 1048460: A triangle has a height of 2x and a base of 7 - 4x.
a) what is the maximum area of the triangle?
b) what value of x gives the maximum area?
Found 2 solutions by rothauserc, ewatrrr:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
Area of triangle(A) = (1/2) * base * height
:
A = (1/2) * (7-4x) * (2x) = 7x - 4x^2
:
we want the first derivative, which is
:
7 -8x
:
set the first derivative = 0 and solve for x
:
7 -8x = 0
:
x = 7/8
:
note that the equation for the Area is a parabola that curves downward,
:
therefore the value of x is a maximum
:
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x = 7/8
:
max Area = 7(7/8) - 4(7/8)^2 = 392/64 - 196/64 = 196/64 = 49/16
:
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Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
A triangle has a height of 2x and a base of 7 - 4x.

A = (1/2)(7-4x)2x
A= - 4x^2 + 7x = -4(x - 7/8))^2 + 4(49/64) |completing the square
a) what is the maximum area of the triangle? 49/16
b) what value of x gives the maximum area? 7/8