SOLUTION: I have a word problem.
"A picture has a square frame that is 2 inches wide. The area of the picture is one-third of the total area of the picture and frame. What are the dimens
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Question 716248: I have a word problem.
"A picture has a square frame that is 2 inches wide. The area of the picture is one-third of the total area of the picture and frame. What are the dimensions of the picture to the nearest quarter of an inch?"
I know that it is a quadratic equation and my teacher said that I have to solve it by completing the square.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
A picture has a square frame that is 2 inches wide. The area of the picture is one-third of the total area of the picture and frame. What are the dimensions of the picture to the nearest quarter of an inch?"
**
let x=length of side of square picture
x^2=area of picture
(x+4)=length of side of square frame
(x+4)^2=total area of picture and frame
..
x^2=1/3(x+4)^2=(x^2+8x+16)/3
3x^2=x^2+8x+16
2x^2-8x-16=0
x^2-4x-8=0
solve for x by completing the square:
(x^2-4x+4)-4-8=0
(x-2)^2=12
take sqrt of both sides
x-2=±√12
x=2±√12
x=2±3.46
x≈-1.46 (reject, x>0)
or
x≈5.5
dimensions of the picture: 5.5 by 5.5 inches
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