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Let X,Y,Z be respectively the areas of r...

Let X,Y,Z be respectively the areas of regular pentagon, regular hexagon and regular heptagon which are inscribed in a circle of radius 1. Then

A

`(X)/(5)lt(Y)/(6)lt(Z)/(7)and XltYltZ`

B

`(X)/(5)lt(Y)/(6)lt(Z)/(7)and XgtYgtZ`

C

`(X)/(5)gt(Y)/(6)gt(Z)/(7)and XgtYgtZ`

D

`(X)/(5)gt(Y)/(6)gt(Z)/(7)and XltYltZ`

Text Solution

Verified by Experts

The correct Answer is:
D

`" Area of Pentagon "=5xx(1)/(2)sin72^(@)=2.377=x`
`" Area of hexagon "=6xx(1)/(2)sin60^(@)=3xx(sqrt3)/(2)=2.598=y`
`" Area of heptagon "=7xx(1)/(2)"sin"(360^(@))/(7)=2.73=z`
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