<PRE><B>Question 286995</B>
A square picture is mounted in a frame 1 cm wide. 
The area of the picture is 2/3 of the total area.
 Find the length of a side of the picture
:
Let s = one side of the square picture
and
s^2 = area of picture
then
(s+2) = side including the frame
and
(s+2)^2 = overall area
:
{{{2/3}}}(s+2)^2 = s^2
multiply both sides by 3
2(s+2)^2 = 3s^2
FOIL
2(s^2 + 4s + 4) = 3s^2
2s^2 + 8s + 8 = 3s^2
0 = 3s^2 - 2s^2 - 8s - 8 
s^2 - 8s - 8 = 0
Use the quadratic formula to solve for s
Positive solution: s ~ 8.9 cm is the side of the picture
:
:
Check this on calc
{{{8.9^2/10.9^2}}} = .666 ~ {{{2/3}}}

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