Question

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?

Answer 1

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:

`(-24 \pm √(24^2 - 4(4)(-37)) )/((4)2)`

`(-24 \pm √(576 +592) )/(8)`

`(-24 \pm √(1168) )/(8)`

`(-24 \pm 34.176)/(8)`

`(10.176)/(8), (-58.176)/(8)` We can get rid of the second option because it is negative.

`1.272`

So the answer is approximately 1.27.