if the area of two similar hexagons are to each other as 5:2, and one side of the first hexagon is 25, what is

Question

if the area 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.

Answer 1

Let x be the other side.
By similarity theorem between solids, we have
25:x = √(5:2)
Solve for x,
x = 25√(2:5) = 5√10

Answer 2

The ratio of linear dimensions would be the square root of the ratio of the areas.
Ratio of linear dimensions: √5:√2
The side of the first would have to be multiplied by the ratio of the second to the first:
(√2/√5)25 = 5√10