FIGURE: Imagine a rectangle within a rectangle. Every side of the interior rectangle is 2 inches from the congruous side of the larger rectangle.
A rectangular picture is surrounded by a border, as shown in the figure above. Without the border the length of the picture is twice the width. If the area of the border is 196 square inches, what is the length, in inches, of the picture, excluding the border?
Answer : 30.
Length of the outer rectangle - L, Breadth of the outer rectangle - B.
Length of the inner rectangle - l, Breadth of the inner rectangle - b.
Now given that - L*B = 196 sq. unit and l = 2b.
Also l = L - 4 and b = B - 4
Hence area of the outer rectangle (border area) = 196 - Area of the inner rectangle
(L * B) = 196 - (l*b)
((l+4) * (b+4)) = 196 - (l*b)
Simplifying => (lb + 4l + 4b + 16) = (196 - lb)
(4l + 4b) = 180
(4(2b) + 4b) = 180
12b = 180
b = 15, l = 30.
Hence the length of the inner rectangle or picture is 30 units. Answer C.
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