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Question

If the angles of a triangle are in the ratio 1:1:4, then the ratio of the perimeter of the triangle to its largest side is

A
3+2:3
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B
3:2
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C
32:2
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D
3+2:2
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Solution

The correct option is A 3+2:3
Let A,B,C be the three angles of the triangle

A1=B1=C4 ...[Given]
B=A and C=4A ...[1]

A+B+C=1800
A+A+4A=1800 ...(Using [1] )
A=300
B=A=300 and C=4A=1200

Using sine rule,
asinA=bsinB=csinC

asin300=bsin300=csin1200

a12=b12=c32

b=a and c=3a

Permeter=a+b+c=a+a+3a=(2+3)a
LargestSide=c=3a

PerimeterLargestSide=(2+3)a3a

=2+33

So, the answer is option (A)

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