A polygon has an area of 144 square inches and one of its sides is 10 inches long. If a second similar polygon has an area of 64 square inches, what is the length of the corresponding side in the second polygon?

Area is proportional to (side length) ^2.

or, put it in another way,

side length is proportional to sqrt (area).

so for the given case,

area = 144, sqrt (area) = 12, side length = 10.

area = 64, sqrt (area) = 8, side length = X

By proportion,

X/8 = 10/12

solve for X

X = (10/12) * 8=20/3 = 6 2/3 = 6.67 (approx.)

So side length of second polygon is approx. 6.67 in., or 6 2/3 inches.