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Question

# Areas of square and rhombus are equal. A diagonal of a rhombus is twice of its other diagonal. If the area of rhombus is 64 sq. cm find the ratio of perimeter of a square and rhombus.

A
3:1
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B
2:5
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C
2:3
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D
5:2
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Solution

## The correct option is B 2:√5Let a be the side of a square andb be the side of a rombus,and d1,d2 be the two diagonals of the rombus.Given,Area of square = Area of rombus⇒a2=d1d22Also,d1=2d2∴a2=2d2d22⇒a2=d2⇒a=d2 and⇒a=d12Area of rhombus is half of the product of the diagonalsd1d22=64⇒d1d2=128⇒(2a)a=128⇒a2=64⇒a=8 cmd1=2a=8×2 =16 cmd2=a =8 cmDiagonals of a rhombus bisect each other at right angles. So, half of both the diagonals and the side of the rhombus make a right angled △∴ Semi-Diagonal d12=162 =8 cmand semi-diagonal d22=82 =4 cm∴82+42=b2⇒b2=64+16⇒b2=80⇒b=√80⇒b=4√5∴ Ratio of perimeter of a square and rhombus =4a:4b =a:b =8:4√5 =2:√5

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