题目信息
The shaded region in the figure above represents a rectangular frame with length 18 inches and width 15 inches. The frame encloses a rectangular picture that has the 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?
A:9
B:
C:
D:15(1 − 
)
)
E:
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已选答案：
正确答案：
A:9
Geometry Rectangles; Area
Let k be the proportionality constant for the fractional decrease from the dimensions of the frame to the dimensions of the picture. That is, let 18k be the length of the picture and let 15k be the width of the picture. We are given that (18)(15) = 2(18k)(15k). Hence, k2 =
and k = 
. Therefore, the length of the picture is 18k = 
.
The correct answer is A.
Let k be the proportionality constant for the fractional decrease from the dimensions of the frame to the dimensions of the picture. That is, let 18k be the length of the picture and let 15k be the width of the picture. We are given that (18)(15) = 2(18k)(15k). Hence, k2 =
and k = . Therefore, the length of the picture is 18k = .The correct answer is A.
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