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?
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. [tex]1.272[/tex]
