Question

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

Answer 1

Answer:

√3/(2+√3)

Step-by-step explanation:

let the angles are 4x,x,x

so sum of angles=4x+x+x=180

6x=180

x=30

so angles are 30,30 and 120

we know that

a/sinA=b/sinB=c/sinC

a/sin30=b/sin30=c/sin120

a/(1/2)=b/(1/2)=c/(sin(90+30)

2a=2b=c/(√3/2)

2a=2b=2c/√3

a=b=c/√3

c=√3a

Perimeter=a+b+c=a+a+√3a=a(2+√3)

so c/perimeter=√3a/a(2+√3)

=√3/(2+√3)

Answer 2

Hope it helps you ...............