A picture frame measures 20 in by 8 in. There is 115 in^2 of the picture showing. The frame is of uniform thickness. Find the thickness of the frame.
Let uniform thickness of frame = x inch
so, length of picture (excluding frame) = (20 - 2x) inch
and, width of picture (excluding frame)= (8 - 2x) inch
Area of picture = (20 - 2x).(8 - 2x)
Also, given, Area of picture $\displaystyle = 115 \;in^2$
so, (20 - 2x).(8 - 2x) = 115
$\displaystyle
4x^2-56x+45=0$
solve,
x = 0.86, 13.14
since thickness of frame should be less than width of frame,
13.14 < 8
so, x cannot be 13.14 in.
therefore thickness of frame = 0.86 inch.
I'm going to assume you mean that the picture is centered in the frame in such a way that the border between the picture and the edge of the frame is of uniform width.
$\displaystyle 115 \ \ in^2$ Area of picture
Diminsions of the picture: $\displaystyle (8-2x)(20-2x)$
$\displaystyle (8-2x)(20-2x)=115$
Solve for x.