ANSWER
I) 5:11
ii) 5:11
iii) 125:1331
EXPLANATION
Let the side lengths be in the ratio:
x:y
This implies that the area will be in the ratio:
[tex] \frac{ {x}^{2} }{ {y}^{2} } = \frac{25}{121} [/tex]
Take positive square root.
[tex] \frac{x}{y} = \sqrt{ \frac{25}{121} } [/tex]
[tex] \frac{x}{y} = \frac{5}{11} [/tex]
Hence the sides are in the ratio:
x:y=5:11
The perimeter of the smaller hexagon is 6×5=30
The perimeter of the larger hexagon is 6×11=66
The ratio of the perimeter is
30:66=5:11
The volume will be in the ratio
5³:11³
125:1331
