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

The correct answer is:

Step1: Finding the angles of the triangle.
Let the ratio of the angles be  and we know that sum of all the angle of a triangle is
Let triangle be  with , and  and the Side opposite to  be  respectively.

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So, the angles of the triangles are
 and  which is 
Hence, , and 
Step2: Finding the ratio of the sides
We know that the sides opposite to the greatest angle will be the greatest. So, side  will greatest.
We have to find 
By using the Sine Rule we get,


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This can be rewritten as
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By flipping the ratios,
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=>from here we get  and  
=>Now 
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