SOLUTION: 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

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
---
2x + 2y = 9
a = xy
---
2y = 9 - 2x
y = (9 - 2x)/2
a = x(9 - 2x)/2
---
a = (9/2)x - xx
a = -xx + (9/2)x
a = -xx + 4.5x
---
the above quadratic equation is in standard form, with a=-1, b=4.5, and c=0
---
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
---
the quadratic vertex is a maximum at: ( x= 2.25, a= 5.0625 )
---
answer:
the frame area is maximum at 5.0625 sq.ft when the frame dimensions are:
L= 2.25 ft
W= 2.25 ft
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
RELATED QUESTIONS
Suppose you want to frame a collage of pictures. You have a 9-ft strip of wood for the... (answered by stanbon)

Lets say you are building a wooden frame for a rhombus shaped mirror. The mirror has... (answered by KMST)

Suppose you want to build a rectangular picture frame where the width is 2 inches more... (answered by josgarithmetic)

You are making a frame for a painting. The painting is 17in by 11in. You want the total... (answered by josgarithmetic,mananth)

You work for a company that produces custom picture frames. A new customer needs to frame (answered by josgarithmetic)

if a photo frame has dimensions 30*20 then what is the length of photo frame . (answered by Fombitz)

eden made a rectangular mosaic using 256 one centimeter square tiles. she used exactly 80 (answered by rothauserc)

Wendy wants to build a frame of uniform width around the outside of her 21cm x 30cm photo (answered by josgarithmetic,Edwin McCravy,mccravyedwin,ikleyn)

a frame maker made a large picture frame using 10 feet of frame molding. If the length of (answered by solver91311)