SOLUTION: a picture is 1 inch longer than it is wide. It is put into a frame 1/2 inch wide. If the area of the frame is 8 inches by itself, how big is the picture?

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Question 309903: a picture is 1 inch longer than it is wide. It is put into a frame 1/2 inch wide. If the area of the frame is 8 inches by itself, how big is the picture?
Answer by stanbon(75887) (Show Source):
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a picture is 1 inch longer than it is wide. It is put into a frame 1/2 inch wide. If the area of the frame is 8 in^2 by itself, how big is the picture?
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Draw the picture of a rectangle inside a rectangle.
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Picture dimentions:, W and L where L = W+1
Area of Picture only : WL
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Picture with frame dimentions: W + 1 and L+1
Area of picture with frame : (W+1)(L+1)
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Equations
Total area - picture area = 8 sq. in.
(W+1)(L+1) - WL = 8
L + W + 1 = 8
L+W = 7
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Substitute W+1 for "L
W+1 + W = 7
2W = 6
W = 3 in (width of the picture)
L = W+1 = 4 in (length of the picture)
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Cheers,
Stan H.
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