Question 72895
 A 5 in. by 7 in. photograph is surrounded by a frame of uniform width. 
The area of the frame equals the area of the photograph. Find the width of the frame.
:
Let x = the width of the frame. 
:
Draw a rough sketch of this, label the picture dimensions, and width of the frame as x.  Note that the dimensions of the frame will be: (7+2x) by (5+2x)
:
Area of the picture: 5*7 = 35 sq in
Area of the frame given as the same, frame = 35 sq in also
Therefore the total area (picture & frame) will be 70 sq in
:
A simple are equation:
(7+2x) * (5+2x) = 70
FOIL
35 + 14x + 10x + 4x^2 = 70
:
4x^2 + 24x + 35 - 70 = 0; subtract 70 from both sides:
:
4x^2 + 24x - 35 = 0
:
Unfortunately this will not factor easily, have to resort to the quad equation:
a = 4; b = 24; c = -35
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
:
{{{x = (-24 +- sqrt( 24^2-4*4*-35 ))/(2*4) }}}
:
{{{x = (-24 +- sqrt( 576 -(-560) ))/(8) }}}
:
{{{x = (-24 +- sqrt( 576 + 560 ))/(8) }}}
:
{{{x = (-24 +- sqrt( 1136 ))/(8) }}}
:
{{{x = (-24 + 33.7046)/(8) }}}; only worry about the positive solution here
:
x = {{{9.7046/8}}}
:
x = 1.213 inches is the width of the frame
:
:
Check our solution
(7 + 2(1.213)) * (5 + 2(1.213))
(7+2.426) * (5+2.426)
9.426 * 7.426 = 69.997 ~ 70