SOLUTION: 3. A picture 8 in. by 12 in. is placed in a frame which has a uniform width. If the area of the frame is equal to the area of the picture, find the width of the frame. Show clear s

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: 3. A picture 8 in. by 12 in. is placed in a frame which has a uniform width. If the area of the frame is equal to the area of the picture, find the width of the frame. Show clear s      Log On

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Question 1172178: 3. A picture 8 in. by 12 in. is placed in a frame which has a uniform width. If the area of the frame is equal to the area of the picture, find the width of the frame. Show clear solutions thanksss!
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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Let the uniform width of the frame be " x " inches.


Then the outer dimensions of the frame are  8+2x and 12+2x.


From the condition, you have this equation

    (8+2x)*(12+2x) - 8*12 = 8*12.


Reduce it to the standard form quadratic equation

    96 + 16x + 24x + 4x^2 - 96 = 96

    4x^2 + 40x - 96 = 0

     x^2 + 10x - 24 = 0

     (x+12)*(x-2) = 0.


This equation has two root, -12 and 2.

Of them , only positive value makes sense.


ANSWER.  The uniform width of the frame is  2 inches.

Solved.