A picture is 5 inches by 7 inches. There is a frame around the picture that is of uniform width. The area of the frame and the picture combined is 72 in2. How wide is the picture frame?

1 Answer

  • We can solve for the area by saying (5 + 2x)(7 + 2x) = 72. We expand to get: 4x^2 + 24x + 35 = 72.
    Now we solve for x:
    4x^2 + 24x - 37 = 0
    Since 37 is prime, we are going to have to use the quadratic formula to solve:
    [tex]\frac{-24 \pm \sqrt{24^2 - 4(4)(-37)} }{(4)2}[/tex]
    [tex]\frac{-24 \pm \sqrt{576 +592} }{8}[/tex]
    [tex]\frac{-24 \pm \sqrt{1168} }{8}[/tex]
    [tex]\frac{-24 \pm 34.176}{8}[/tex]
    [tex]\frac{10.176}{8}, \frac{-58.176}{8}[/tex] We can get rid of the second option because it is negative.

    So the answer is approximately 1.27.