Question

Two pentagons are similar. The area of one of the pentagons is 9 times

that of the other. Determine the ratios of the lengths of the corresponding
sides and the perimeters of the pentagons.​

Answer 1

The ratios of the lengths of the corresponding sides of the two pentagons is 3:1

The ratios of the perimeters of the two pentagons is 3:1

Explanation:

Let the first pentagon be X and the second pentagon be Y.

Ratio of area of the two pentagons is
`(A1)/(A2) = (9)/(1)`

Ratio of sides of the pentagon is equal to

`(S1)/(S2) = \sqrt{(A1)/(A2) }\\=\sqrt{(9)/(1) } \\=(3)/(1)`

Ratio of perimeters is equal to ration of sides

Hence,

`(P1)/(P2) = (3)/(1)`