Question

Two hexagons have an area ratio of 36:49. Find the ratio of their perimeters.​

Answer 1

Ratio of their perimeters is 6:7

Explanation:

Ratio of Area of Hexagon = 36: 49

We need to find ratio of their perimeters

The formula used to find Area of Hexagon is:
`Area\: of\: Hexagon=(3√(3) )/(2)a^2`

So, we can write:

`Area\: of\: Hexagon\: 1: Area\: of\: Hexagon\: 2=36:49\\(3√(3) )/(2)a_1^2:(3√(3) )/(2)a_2^2=36:49\\((3√(3) )/(2)a_1^2)/((3√(3) )/(2)a_2^2) =(36)/(49) \\(a_1^2)/(a_2^2)= (36)/(49)\\Taking\:square\:root\\\sqrt(a_1^2)/(a_2^2)}=\sqrt{(36)/(49)}\\(a_1)/(a_2)=(6)/(7)`

So, we get a₁=6 and a₂=7

Now, finding ratio of perimeters:

The formula used is:

`Perimeter\:of\:hexagon=6a`

Ratio will be:

`Perimeter\:of\:hexagon\:1:Perimeter\:of\:hexagon\:2\\6a_1:6a_2\\Put\;a_1=6,a_2=7\\6(6):6(7)\\=(6(6))/(6(7))\\=(6)/(7)`

So, Ratio of their perimeters is 6:7