Question

a carpenter is building a rectangular room with a fixed perimeter of 92ft. what demensions would yeild the maximum area? i got 529ft is that correct?

Answer 1

92=2l+2w
46=l+w
23^2=529 I dont know if I done this right or not but thats the way i was working it

Answer 2

A square will give the largest area. If the perimeter is 92 each side is 23 so the area is 23^2

Answer 3

Let the width be w
Let the length be l
2(w+l) = 92
w = 46 - l

l(46 - l)

23^2 = 529

Answer 4

The correct way to do it is to say the sides of the rectangle are x and 46-x so the area is x(46-x) Take the first derivative, set it to 0 and solve for x.

Answer 5

i think i did this wrong, the length that would yield the maximum area is what? would it still be 529? or do i need to start over

Answer 6

It would be 23

Answer 7

would you mind showing me how you got that

Answer 8

Are you taking calculus?

Answer 9

You don't need calculus because the equation is a parabola, the maximum is the vertex

Answer 10

algebra and my teacher thinks i know how to do all this stuff lol I DONT

Answer 11

That is correct but it is just as easy to take the derivative if she is taking calculus.

Answer 12

i wished i didnt have to take any math lol my math teacher in high school made me not like math

Answer 13

ok so now i got to find the width

Answer 14

area = x(46-x) = -x^2+46x
The x coordinate for the vertex of a parabold is -b/2a which equals -46/-2 = 23

Answer 15

ok then. You should write that the area is x(46-x) or 46x-x^2. That is a parabola. The x coordinate of its vertex is -b/2a or -46/-2 or 23. So one side is 23 and the other side is 46-23 which is also 23. So it is a square---a 23 by 23 square.

Answer 16

so the length would be my original answer of 529?

Answer 17

no its l=23
w=23
maximum =529