SOLUTION: Could you please help me with this word problem? You are making a square frame of uniform width for a square picture that has side lengths of 2 feet. The total area of the fr

Question 526024: Could you please help me with this word problem?
You are making a square frame of uniform width for a square picture that has side lengths of 2 feet. The total area of the frame is 5 square feet. What is the length of the sides of the frame?
Kamsahamnida! (Thank You!)

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
You are making a square frame of uniform width for a square picture that has side lengths of 2 feet. The total area of the frame is 5 square feet. What is the length of the sides of the frame?
------------
picture area = 2*2 = 4 sq. ft.
-----
Let the uniform with of the frame be "x".
The outer dimensions of the frame are (2+2x)ft by (2+2x) ft
----
Area of the whole picture with frame = (2+2x)^2 = 4+8x+4x^2
---
So, area of the frame alone is 4x^2+8x+4-4 = 4x^2+8x
---
Equation:
Solve for "x":
4x^2+8x = 5
4x^2+8x-5 = 0
Positive solution:
x = [-8 + sqrt(64-4*4*-5)]/8
----
x = [-8 + sqrt(144)]/8
-----
x = [-8+12]/8
---
x = 1/2 ft
----
Length of the out sides of the frame = (2+2x) = 2+1 = 3 ft.
=============================
Cheers,
Stan H.
=============================
RELATED QUESTIONS
Could you please help with the following problem: A picture 9 inches wide and 12 inches... (answered by stanbon)

Could you please help me with this word problem? Thank you in advance. The dimensions of (answered by josmiceli)

Could you please help me with this problem? I have a hard time figuring out how to set... (answered by jim_thompson5910,josmiceli)

"You are making a frame of uniform width for a picture that is to be displayed at the... (answered by ankor@dixie-net.com)

Hi, I'm having trouble solving and figuring out what to do with this problem: A... (answered by mananth)

Could someone please help me with this problem. A rectangular picture frame is 5 inches... (answered by josmiceli)

this one is tough.. you are making a coffee table with a glass top surrounded by a cherry (answered by edjones)

Sirs/Madams, Kindly help my son in solving one item in his assignment. He was able to... (answered by jsmallt9)

this one is tough.. you are making a coffee table with a glass top surrounded by a cherry (answered by scott8148)