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# Two rectangles are drawn such that they share a center and that the sh

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Math Expert
Joined: 02 Sep 2009
Posts: 50580
Two rectangles are drawn such that they share a center and that the sh  [#permalink]

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14 Sep 2018, 00:25
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(N/A)

Question Stats:

89% (01:44) correct 11% (00:00) wrong based on 9 sessions

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Two rectangles are drawn such that they share a center and that the shaded rectangle is 2 inches from the edge of the larger rectangle as shown above. If the perimeter of the shaded rectangle above is 27 inches, then the area of the larger rectangle is how many square inches more than the area of the shaded one?

A. 16
B. 53
C. 54
D. 70
E. 108

Attachment:

image040.jpg [ 5.48 KiB | Viewed 248 times ]

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Re: Two rectangles are drawn such that they share a center and that the sh  [#permalink]

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14 Sep 2018, 00:52
Bunuel wrote:

Two rectangles are drawn such that they share a center and that the shaded rectangle is 2 inches from the edge of the larger rectangle as shown above. If the perimeter of the shaded rectangle above is 27 inches, then the area of the larger rectangle is how many square inches more than the area of the shaded one?

A. 16
B. 53
C. 54
D. 70
E. 108

Attachment:
image040.jpg

Let the length and breadth of the shaded rectangle be l and b respectively.
length and breadth of the larger rectangle = l+4 and b+4 respectively.
Perimeter of shaded rectangle =2(l+b) = 27

Difference of areas = (l+4)(b+4)-lb
=lb+4(l+b)+16-lb = 2x27+16 = 70 [ putting value of 2(l+b) = 27]
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Joined: 02 Sep 2015
Posts: 42
Two rectangles are drawn such that they share a center and that the sh  [#permalink]

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14 Sep 2018, 10:28
Length of shaded rectangle = L
Given:
Perimeter of shaded rectangle = 2(L + B) = 27
Length of outer rectangle = L + 4
Breadth of outer rectangle = B + 4

We need to find
= Area of outer rectangle - Area of shaded region
= $$(L + 4) * (B + 4) - LB$$
= $$LB + 4L + 4B + 16 - LB$$
= $$4(L + B) + 16$$
= $$2 * 2(L + B) + 16$$
= $$2 * 27 + 16$$
= 70

Two rectangles are drawn such that they share a center and that the sh &nbs [#permalink] 14 Sep 2018, 10:28
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