Let x be the
width of the frame.
Area of the picture is 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 equation would be made and it will look like this: (7+2x) * (5+2x) =
70
Using the FOIL
method
35 + 14x + 10x + 4x^2 = 70
4x^2 + 24x + 35 - 70 = 0; subtract 70 from both sides:
4x^2 + 24x - 35 = 0
unluckily this will not factor easily, so we should use the quadratic equation:
where: a = 4; b = 24; c = -35
x = -b sqrt b^2 – 4*a*c divided by 2 * a
x
= -24 ±
sqrt 24^2 -4*4*(-35) divided by 2*4
x = -24 ±sqrt 576 -
-(560) divided by 8
x = -24 ± sqrt 576 + 560 divided by 8
x = -24 ± sqrt1136
divided by 8
x = -24 + 33.7046 divided by 8
x = 9.7046 divided by 8
x =1.213 inches is the answer
