John has 300 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). He wants to maximize the area of his patio (area of a rectangle is length times width). What should the dimensions of the patio be, and show how the maximum area of the patio is calculated from the algebraic equation.
Show clearly the algebraic steps which prove your dimensions are the maximum area which can be obtained.
Answer:
Show work in this space.
SERIOUS ANSWERS ONLY!!!
2006-06-20 06:44:45 · 6 answers · asked by korr1121 3 in Education & Reference ➔ Homework Help
All right listen, I'm in college, so this is from a college course and asking for help is not cheating.
2006-06-20 06:49:52 · update #1
Thanks for the answer, but 75x75 is a square and I need a rectangle.
2006-06-20 07:08:37 · update #2
So we know this:
P = 2w + 2L A = WL
and we can then get to this point.
300 = 2W + 2L A/W = L
The plan is to get an equation with A that we can find the max of.
The best would be a quadratic equation.
Substitute A/W for L
300 = 2(A/W) + 2W
300W = 2A + 2W^2
-2W^2 + 300W = 2A
-W^2 + 150W = A
Now we can find the max by finding the vertex which is -b/2a
-(150/(2*-1))
75
So W = 75 which implies L = 75
2006-06-20 07:11:11 · answer #1 · answered by theFo0t 3 · 4⤊ 0⤋
To answer questions in which you need to find the maximum area if you already have the perimeter, you have to try to make the shape of the patio as close to a square as possible. For this problem, it is easy.
300 feet/ 4 = 75 feet
For these problems, using an algebraic equation gets messy, use common sense (divide the perimeter by 4 and you'll get the length of the sides of the square which will give you the greatest area)
Therefore, the dimensions of the patio should be 75 feet by 75 feet.
2006-06-20 07:03:57 · answer #2 · answered by MathTeen 2 · 0⤊ 0⤋
Sorry, having other people do your work is cheating. It was cheating when you did it in high school. It's cheating when you're doing it now in college. It will be cheating when you do it in your career and marriage. Why are you wasting mummy and daddy's money on tuition?
And why are you doing 5th grade math in college? I feel bad if you have a disability and I gave you a hard time.
2006-06-20 07:01:39 · answer #3 · answered by Dixon T 1 · 0⤊ 0⤋
I'll give you a serious answer. If you cheat in school, you will fail in life. The joke's on you!
2006-06-20 06:48:33 · answer #4 · answered by Anonymous · 0⤊ 0⤋
A square is a rectangle!
All squares are rectangles.
Some rectangles are squares.
2006-06-20 08:09:57 · answer #5 · answered by MsMath 7 · 0⤊ 0⤋
sorry, what grade r u??
2006-06-20 06:48:06 · answer #6 · answered by just me!!!! 3 · 0⤊ 0⤋