Asquare picture has a one-inch frame. if the area of the frame alone is 48 square inches, what is the area of the picture?

The area of the picture alone is 132 sq. in.

Let x be the side length of the square.  Then (x+2) is the side of the square after the frame has been added.  The area of the picture with frame is given by

(x+2)(x+2).  The area of just the frame is given by (x+2)(x+2)-x*x:

(x+2)(x+2)-x*x=48
x²+x*2+2*x+2*2-x² = 48
x²+2x+2x+4-x² = 48
4x + 4 = 48

Subtract 4 from both sides:
4x = 44

Divide both sides by 4:
x = 11

This means the area of the square is 11(11) = 132.