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Re: The shaded region in the figure above represents a rectangular frame [#permalink]
Top Contributor
The shaded region in the figure above represents a rectangular frame with a length of 20 inches and a width of 16 inches. The frame encloses a rectangular picture that has same area as the frame itself. If the length and width of the picture have the same ratio as the length and width of the frame, what is the length of the picture, in inches?

it's given that the length and width of the picture have the same ratio as the length and width of the frame

l/b = 20/16 = 5/4

Let's assume, l = 5k and b = 4k

Its given that Area of the picture = Area of the frame (Shaded region)

Area of the picture =\( l * b = 5k*4k = 20 k^2\)

Area of the frame (Shaded region) = 20*16 - Area of the picture

Therefore,
\(20*16 - 20 k^2 = 20 k^2\)
\(20*16 = 2 * 20 k^2\)
\(k^2 = 8\)
\(k = 2\sqrt{2}\)

length of the picture =\( 5 k = 5 * 2\sqrt{2} = 10\sqrt{2}\)

Option E is the correct answer.

Hope this helps,
Clifin J Francis,
GMAT SME
GMAT Club Bot
Re: The shaded region in the figure above represents a rectangular frame [#permalink]
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