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A picture measuring 2 inches by 3 inches is placed inside a frame. The width
of the border between the picture and the frame is the same around the entire picture.
If the area of the border and the picture is 72 square inches, what is the width
of the border?
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sqdancefan

Answer:

  3 inches

Step-by-step explanation:

You want the width of the uniform border around a 2" by 3" picture if the framed picture has an area of 72 square inches.

Difference

The dimensions of the picture tell you the difference between the height and width of the framed picture will be 3 -2 = 1 inch.

Factors

The area of the frame is the product of its height and width. This means we want to find numbers that multiply to give 72:

  72 = 1·72 = 2·36 = 3·24 = 4·18 = 6·12 = 8·9

The factors of the area value that differ by 1 are 8 and 9. This means the framed picture is 8 inches by 9 inches. These values include the picture dimensions plus twice the frame width:

  frame width = (8 in - 2 in)/2 = 3 in

The width of the border around the picture is 3 inches.

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