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Question

Find the ratio of perimeters and areas of lands ABCD to ABFE. (Given AE = 2AD)


A

Perimeter ratio = 1 ; Area ratio = 12

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B

Perimeter ratio = (x+y)2(x+2y) ; Area ratio = 12

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C

Perimeter ratio = (x+y)(x+2y) ; Area ratio = 1

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D

Perimeter ratio = 12 ; Area ratio = 1

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Solution

The correct option is C

Perimeter ratio = (x+y)(x+2y) ; Area ratio = 1


Perimeter (ABCD) = 2 (AB + AD) = 2 (x + y)

Perimeter (ABFE) = 2 (AB + AE) = 2 (x + 2y) (Since AE = 2AD)

So, perimeter ratio = Perimeter(ABCD)Perimeter(ABEF)=2(x+y)2(x+2y)=x+y(x+2y)

Area (ABCD) = 2 (AB × AD) = 2xy

Area (ABFE) = Area (ABCD) [Both the parallelorgrams ABCD and ABFE are lying on the same base and between the same parallel lines]

So, area ratio = Area(ABCD)Area(ABEF)=1


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