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In triangle ABC, angle A=pi/2, b=4, c=...

In `triangle ABC,` `angle A=pi/2,` `b=4,` `c=3`, then the value of `R/r` is equal to

A

`5/2`

B

`7/2`

C

`9/2`

D

`35/24`

Text Solution

Verified by Experts

We have,
`angleA=pi/2`
`rArrBC^(2)=CA^(2)+AB^(2)`
`rArra^(2)=b^(2)+c^(2)rArra^(2)=16+9rArra=5`
`thereforeR=a/(2sinA)=5/(2sinpi/2)=5/2`
Also, `Delta=1/2bcsinA=1/2xx4xx3xxsinpi/2=6`
and, `2s=a+b+c=5+4+3=12rArrs=6`
`thereforer=(Delta)/s=6/6=1`
Hence, `R/r=5/2`
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