Question

If the ratio of the angles in the triangle is 1:2:7 then find the ratio of longest side to the smallest side

Answer 1

Solution :

It quite simple :

Ratio of angles in a triangle = 1 : 2 : 7

Now ,

Ratio of longest side to the smallest

side = 1 : 7

OR

Let A , B and C are three angles of

∆ABC,

A : B : C = 1 : 2 : 7 ( given )

Let A = x ,

B = 2x ,

C = 7x ,

A + B + C = 180°

[ Angle sum property ]

x + 2x + 7x = 180

=> 10x = 180

=> x = 180/10

=> x = 18

Therefore ,

A = x = 18°

B = 2x = 2 × 18 = 36°

C = 7x = 7 × 18 = 126°

Now ,

Ratio of longest side to the smallest

side = 126 : 18

= ( 7 × 18 ) : ( 1 × 18 )

= 7 : 1

Answer 2

Let the angles are X , 2X and 7X.

As we know , sum of three angles of a triangle is equal to 180.

So,

X + 2X + 7X = 180

10X = 180

X = 18

First angle = X = 18

Second angle = 2X = 36

And,

Third angle = 7X = 7 × 18 = 126.

Ratio of longest side to the smallest side = 126 : 36 = 63 : 18 = 21 : 6 = 7 : 2