Question 823564: Suppose you want to frame a collage of pictures. You have a 9-foot strip of wood for the frame. What dimensions of the frame give you the maximum area for the collage? What is the maximum area?
Please help! I just can't wrap my brain around this one and I know I should easily be able to solve it but I've spent almost 15 minutes on it and I'd like to my other homework so please help. Thank you!
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
perimeter = 2x + 2y = 9
area = xy
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2x + 2y = 9
a = xy
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2y = 9 - 2x
y = (9 - 2x)/2
a = x(9 - 2x)/2
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a = (9/2)x - xx
a = -xx + (9/2)x
a = -xx + 4.5x
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the above quadratic equation is in standard form, with a=-1, b=4.5, and c=0
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
-1 4.5 0
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic vertex is a maximum at: ( x= 2.25, a= 5.0625 )
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answer:
the frame area is maximum at 5.0625 sq.ft when the frame dimensions are:
L= 2.25 ft
W= 2.25 ft
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