Question 136228
Width of the picture:  x
Length of the picture: x + 10
Area of just the picture:  {{{x(x+10)=x^2+10x}}}


Width of the picture with frame:  x + 2
Length of the picture with frame:  x + 12
Area of picture and frame:  {{{(x+2)(x+12)=x^2+14x+24}}} and this is 40 greater than the area of just the picture, so:


{{{x^2+14x+24=x^2+10x+40}}}


Collecting terms:
{{{4x=16}}}


{{{x=4}}} is the width and {{{4 + 10= 14}}} is the length of the original picture.  With the frame, the width is 6 and the length is 16.

4 * 14 = 56
6 * 16 = 96
And the difference is 40, answer checks.