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.
:
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