Question 548513: A picture frame measures 26 in. by 24 in.. There is 575 in. squared of picture showing. The frame is of uniform thickness. Find the thickness of the frame.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A picture frame measures 26 in. by 24 in..
There is 575 in. squared of picture showing.
The frame is of uniform thickness. Find the thickness of the frame.
:
Let x = the width of the frame
then
(26-2x) by (24-2x) is the dimensions of the pictures, which is 575 sq/in
therefore, the area equation:
(26-2x)*(24-2x) = 575
FOIL
624 - 52x - 48x + 4x^2 = 575
Combine like terms to form a quadratic equation:
4x^2 - 100x + 624 - 575 = 0
4x^2 - 100x + 49 = 0
We can us the quadratic formula, but this will factor to
(2x-49)(2x-1) = 0
two solutions, but only one will make sense
2x = 49
x = 49/2
x = 24.5", obviously this could not be the width of frame
and
2x = 1
x = .5 inch is the reasonable width of the frame
:
:
We can confirm this by finding the area using x=.1, then 2x = 1, so we have
(26+1)(24+1) = 675 for the overall area, like was given
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