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 your answer to two
decimal places.
A. 3.16
B. 10.00
C. 15.81
D. 250.00
I tried to do this setting up a proportion and got B.10.00, however this answer proved to be incorrect. Help please.
areas scale as square of length ratio
so
5/2 in area ---> sqrt(5)/sqrt(2) in length
so
25 * sqrt 2/sqrt 5 = 15.813883
think square 3 meters on each side
area = 3*3 = 9
then square 6 meters on a side, double
area = 6*6 = 36 or four times
length ratios = 2
area ratios = 4
2^2 = 4
the question asked for the corresponding side, not the area. So, 10.00 is the correct answer.
oops. My bad. I neglected to read that the areas were 5:2, not the sides.
Go with Damon. Right, as usual.
Thank you so much for the help Damon and Steve!
To solve this problem, we can set up a proportion using the ratio of the areas of the two hexagons.
The ratio of the areas is given as 5:2. This means that the area of the first hexagon is 5/2 times the area of the second hexagon.
The formula to calculate the area of a regular hexagon is A = (3√3/2) * s^2, where A is the area and s is the length of the side.
Given that one side of the first hexagon is 25, we can calculate its area using the formula:
A1 = (3√3/2) * (25^2) = (3√3/2) * 625 ≈ 1082.532
Let's denote the corresponding side of the second hexagon as x. Then, the area of the second hexagon is:
A2 = (3√3/2) * x^2
Now, we can set up the proportion:
A1/A2 = 5/2
(3√3/2) * 625 / [(3√3/2) * x^2] = 5/2
Simplifying the equation, we get:
625 / x^2 = 5/2
To solve for x, let's cross-multiply and solve for x^2:
625 * 2 = 5 * x^2
x^2 = (625 * 2) / 5 = 250
Now, take the square root of both sides to find x:
x = √250 ≈ 15.81
Therefore, the corresponding side in the other hexagon is approximately 15.81.
Rounding it to two decimal places, the correct answer is C. 15.81.