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Question

The angles A,B and C of a triangle ABC are in A.P. and a:b=1:3. If c=4 cm, then the area (in sq.cm) of this triangle is:

A
43
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B
23
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C
43
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D
23
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Solution

The correct option is B 23
Given,
The angles of ABC are in A.P.
sum of angles of a triangle =π
A+B+C=π & 2B=A+C
3B=πB=π3
A+C=2π3σ
ab=13
2RsinA2RsinB=13
sinAsinπ3=13
sinA=12
A=30
a=2,b=23,c=4

Area=12×23×2=23

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