If areas of 2 similar hexagons are to each other as 5:2, and

[HomeWork14]

I would like to know if my work and answer are the correct. Thank you!

Question: If the areas of two similar hexagons are to each other as 5:2, and one side of the first hexagon is 25, what is the corresponding side in the other hexagon? Round answer to two decimal place.

My work:

Formula: A1/A2 = X2 ( to the 1st power) / X2 ( squared)

5/2 =25/X2 (squared) = 3.16 <= My answer.

 

[Deleted member 4993]

If the areas of two similar hexagons are to each other as 5:2, and one side of the first hexagon is 25, what is the corresponding side in the other hexagon? Round answer to two decimal place.

Formula: A1/A2 = X1 (squared) / X2 ( squared)

X2 (squared) = X1 ( squared) * A2/A1 = 625 * 2/5 = 250

Now finish it...

 

[soroban]

Re: If areas of 2 similar hexagons are to each other as 5:2,

Hello, HomeWork14!

If the areas of two similar hexagons are to each other as 5:2,
and one side of the first hexagon is 25, what is the corresponding side in the other hexagon?
Round answer to two decimal place.

The ratio of the areas of two similar figures is equal to ratio of the squares of their sides.

The sides of the hexagons are: \(\displaystyle 25\) and \(\displaystyle x\).

Then: \(\displaystyle \L\:\frac{25^2}{x^2} \:=\:\frac{5}{2}\;\;\Rightarrow\;\;5x^2\:=\:1250\;\;\Rightarrow\;\;x^2\:=\:250\)

Therefore: \(\displaystyle \L\:x \:=\:\sqrt{250} \:=\:5\sqrt{10}\)