Question

Two similar hexagons have areas of 36 square inches and 64 square inches. The ratio of the corresponding sides of the hexagons is _____.

Answer 1

Answer:  The answer is 3 : 4.

Step-by-step explanation:  Given that the two similar hexagons have areas  of 36 square units and 64 square units. We are to find the ratio of the corresponding sides of the hexagons.

We know that the area of a regular hexagon with side of length 'a' units is given by

$A=\dfrac{3\sqrt 3}{2}a^2.$

Let, A and B be the areas of the two hexagons and 'a' and 'b' be the lengths of the corresponding sides. Then, we have

$A=\dfrac{3\sqrt 3}{2}a^2,\\\\\\B=\dfrac{3\sqrt 3}{2}b^2.$

According to the question,

$A:B=36:64\\\\\Rightarrow \dfrac{\frac{3\sqrt 3}{2}a^2}{\frac{3\sqrt 3}{2}b^2}=\dfrac{36}{64}\\\\\\\Rightarrow \dfrac{a^2}{b^2}=\dfrac{9}{16}\\\\\Rightarrow \dfrac{a}{b}=\dfrac{3}{4}\\\\\Rightarrow a:b=3:4.$

Thus, the required ratio is 3 : 4.

Answer 2

sqrt(36) = 6

sqrt(64) =8

 proportion is 6/8 reduces to 3/4