A polygon has an area of 225 square meters. A similar polygon is created with an area that is triple the first. By what factor is the length of each side increased?

The area of the original polygon is:

A = 225 m ^ 2

The similar polygon area is:

A ' = (k ^ 2) * (A)

Substituting values:

3 * 225 = (k ^ 2) * (225)

Clearing k we have:

k ^ 2 = 3

k = (3) ^ (1/3)

Answer:

The length of each side increased by:

k = (3) ^ (1/3)