# geometry

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the ratio of the perimeter of two similar squares is 5 to 4. If the area of the smaller square is 32 square units, what is the area of the larger square?

• geometry -

The ratio of the perimeters is equal to the ratio of their sides
if the perimeters are in the ratio of 5:4, then the sides are in the ratio of 5:4

the ratio of areas of similar shapes is proportional to the square of their sides, so

x/32 = 5^2/4^2 = 25/16
x = 32(25/16) = 50

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