Question

In the picture above, the perimeter of the starfish is 30 centimeters. This original picture is to be enlarged in both dimensions to an image that is similar to the original picture. If the area of the enlarged image is 9 times the area of the original picture, what is the perimeter in centimeters of the starfish in the enlarged image?

Can anyone show me how to solve this, please?

Answer 1

the ratio of length of two similar figure, we call scale factor
(scale factor)^2 => area ratio
(scale factor)^3 => volume ratio

the area of the enlarged image is 9 times the area of the original
√(1/9) = 1/3 => scale factor

the perimeter of the starfish is 30 centimeters
then
the perimeter in centimeters of the starfish in the enlarged image
will be 30 cm*3 = 90 cm