The ratio of the perimeters 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?

Answer 1

Since both the length of sides and perimeter are linear

the perimeters would be in that same ratio as the sides.
So the sides are in the ratio of 5:4

The ratio of areas is equal to the square of their corresponding sides.
so
A/32 = 5^2 / 4^2
A = 32(25)/16 = 50

Answer 2

If Smaller square = 32
Perimeter of Small Square = 4x
Perimeter of Larger Square = 5x
Perimeter Of Small Square = 4L
4x = 32
x = 32 / 4
x = 8
Then
5x = 5(8)
5x = 40