"a rectangular painting measures 12 inches by 16 inches and is surrounded by a frame of uniform width around the four edges. the perimeter of the rectangle formed by the painting and its frame is 72 inches. determine the width of the frame.\"

Area of this rectangular painting=lenght x width.
Data:
lenght=16 in.
width=12 in.

Area (rectangular painting)=16 in * 12 in=192 in².

x=width of the frame.
lenght of the frame=16+2x
width of the frame=12+2x

Perimeter of the painting and its frame=2(16+2x)+2(12+2x)

We can suggest this equation:
2(16+2x)+2(12+2x)=72
32+4x+24+4x=72
4x+4x=72-32-24
8x=16
x=16/8
x=2

the width of the frame is 2 in.