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A picture 8 inches by 12 inches is placed in a frame of uniform width. If the area of the frame equals the area of the picture, find the width of the frame

 Feb 17, 2020
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Let the width of the frame  be = W

 

So....the   area of the picture and frame =  (8 + 2W) (12 + 2W)

 

And  this  whole area  -  the area of the picture =  the area of the  picture.....so....

 

(8 + 2W) ( 12 + 2W)  - 96 =  96     

 

96 + 24W + 16W + 4W^2  - 96 = 96    simplify

 

 

4W^2 + 40W  - 96  =  0        divide through by 4

 

W^2  + 10W  - 24  =  0     factor

 

(W + 12) ( W - 2)   =0

 

Setting each factor to  0  and solving for W produces   

 

W = -12 inches   [ reject]

 

or

 

W = 2 inches   [ correct answer ]

 

 

 

cool cool cool

 Feb 17, 2020

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