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 $= 115 \;in^2$

so, (20 - 2x).(8 - 2x) = 115

$
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.

3. Originally Posted by mathdummy22
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.
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.

$115 \ \ in^2$ Area of picture

Diminsions of the picture: $(8-2x)(20-2x)$

$(8-2x)(20-2x)=115$

Solve for x.