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In DeltaABC ,if A:B:C =3:5:4,then a+b+sq...

In `DeltaABC` ,if A:B:C =`3:5:4`,then `a+b+sqrt2c=`

A

2b

B

2c

C

3b

D

3a

Text Solution

Verified by Experts

Let A = 3x, B = Sx and C = 4x. Then,
A+ B+C 180 `rArr` x=15°
`thereforeA=45^(@),B=75^(@)` and `C=60^(@)`
Now,
`a/(sinA)=b/(sinB)=c/(sinC)=2R`
`rArra=sqrt2R,b=(sqrt3+1)/(sqrt2)` R and `c=sqrt3R`
`rArra+b+sqrt2c=sqrt2R+(sqrt3+1)/(sqrt2)R+sqrt6R`
`rArra+b+sqrt2c=(3R+sqrt3R+2sqrt3R)/(sqrt2)=3((sqrt3+1)/(Sqrt2))R=3b`
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