Question 1026358: Please help me with the following word problem:
The perimeter of a rectangle is 64 cm.
(a)
If the width of the rectangle is x cm, give a formula for y, the height of the rectangle in cm, in terms of x.
For this one I got y=32-x, but the answer is needed for part b so I thought I should include it.
(b)
Using your answer in part (a), give a formula for A, the area in cm^2, in terms of the width x.
For this one, I tried to substitute the formula for y into the equation for the perimeter: 2x+2y=64. This didn't work because when I substituted that formula into the equation, the equation didn't allow me to solve for y because it zeroed out.
(c)
Find the lengths of the sides of the rectangle giving the maximum area. What is the maximum area?
For this one, I couldn't do it since the substitution in the previous problem didn't help. I also don't understand what maximum area means.
Thank you for the help and your time :)
Found 2 solutions by rothauserc, josmiceli:
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! a) y = 32-x is correct
:
b) Area(A) = x * y, then
A = x * (32-x) = 32 -x^2
:
c) b) is the formula of a parabola that curves downward, so the maximum area will be y coordinate of the parabola's vertex.
The x is -b/2a which is -32 / (2 * (-1)) = 16 and y is 32 - 16 = 16
:
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x = 16 cm
y = 16 cm
Max area is 16^2 = 256 cm^2
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Answer by josmiceli(19441)  (Show Source):
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