Ratio of sides

If the angles of a triangle are in the ratio of !!4:1:1!! then the value of:

!!("Perimeter of triangle")/"Largest side"=!!

  • !!1+sqrt(3)/2!!
  • !!sqrt(3)/2!!
  • !!1+2/sqrt(3)!!
  • !!2/sqrt(3)!!

Solution:

In this question since we know the ratio of angles we can say the angles are !!120,30,30!! respectively.

Now to find the ratio of sides, we need the length of each side.

In triangles there is a sine rule which says:

!!a= r sin A!!

!!b= r sin B!!

!!c= r sin C!!

Here !!a,b,c!! are the length of the sides and !!A,B,C!! are the angles of the triangle, r is a constant.

So we have

!!(a+b+c)/a!!

!!=1+(b+c)/a!!

!!= 1+ (sin30+sin30)/sin(120)!!

!!=1+2/sqrt(3)!!

We can get the same result using the cosine rule.
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