Question

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

Answer 1

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: $Area\: of\: Hexagon=\frac{3\sqrt{3} }{2}a^2$

So, we can write:

$Area\: of\: Hexagon\: 1: Area\: of\: Hexagon\: 2=36:49\\\frac{3\sqrt{3} }{2}a_1^2:\frac{3\sqrt{3} }{2}a_2^2=36:49\\\frac{\frac{3\sqrt{3} }{2}a_1^2}{\frac{3\sqrt{3} }{2}a_2^2} =\frac{36}{49} \\\frac{a_1^2}{a_2^2}= \frac{36}{49}\\Taking\:square\:root\\\sqrt\frac{a_1^2}{a_2^2}}=\sqrt{\frac{36}{49}}\\\frac{a_1}{a_2}=\frac{6}{7}$

So, we get a₁=6 and a₂=7

Now, finding ratio of perimeters:

The formula used is:

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

Ratio will be:

$Perimeter\:of\:hexagon\:1:Perimeter\:of\:hexagon\:2\\6a_1:6a_2\\Put\;a_1=6,a_2=7\\6(6):6(7)\\=\frac{6(6)}{6(7)}\\=\frac{6}{7}$

So, Ratio of their perimeters is 6:7