Question

A 5 in by 7in 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

Answer 1

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