Answer:
Ratio of their perimeters is 6:7
Step-by-step 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: [tex]Area\: of\: Hexagon=\frac{3\sqrt{3} }{2}a^2[/tex]
So, we can write:
[tex]Area\: of\: Hexagon\: 1: Area\: of\: Hexagon\: 2=36:49\\\frac{3\sqrt{3} }{2}a_1^2:\frac{3\sqrt{3} }{2}a_2^2=36:49\\\frac{\frac{3\sqrt{3} }{2}a_1^2}{\frac{3\sqrt{3} }{2}a_2^2} =\frac{36}{49} \\\frac{a_1^2}{a_2^2}= \frac{36}{49}\\Taking\:square\:root\\\sqrt\frac{a_1^2}{a_2^2}}=\sqrt{\frac{36}{49}}\\\frac{a_1}{a_2}=\frac{6}{7}[/tex]
So, we get a₁=6 and a₂=7
Now, finding ratio of perimeters:
The formula used is:
[tex]Perimeter\:of\:hexagon=6a[/tex]
Ratio will be:
[tex]Perimeter\:of\:hexagon\:1:Perimeter\:of\:hexagon\:2\\6a_1:6a_2\\Put\;a_1=6,a_2=7\\6(6):6(7)\\=\frac{6(6)}{6(7)}\\=\frac{6}{7}[/tex]
So, Ratio of their perimeters is 6:7
