Consider 3 squares, A, B, and C. Where the perimeter of square A is 2/3 the perimeter of square B and the perimeter of square B is 2/3 the perimeter of square C. If the area of square A is 16 what is the area of square C?

Question

anonymous · Answer

A= 2/3 * B
B = 2/3 * C

A = 16
2/3 * B = 16    / * 3 / 2
B = 48/ 2 --> B = 24
B = 2/3 * C
3*B /2 = C
C = 3* 24/ 2 = 36

anonymous · Answer

If the area of square A is 16, then its side length is 4, so its perimeter is also 16. That makes the perimeter of B 24, and the perimeter of C 36. If the perimeter of C is 36, then its side length is 9, so its area is 81.

anonymous · Answer

So who is right?

anonymous · Answer

We both are, he just only went as far as finding the perimeter of C.

anonymous · Answer

how do you know that is the perimeter?

anonymous · Answer

The perimeter of a square is $4s$, where $s$ is the side length. Since the area function for a square is $A=s^2$, we got that the side length of A was 4 by square rooting 16. Then we multiply by 4 to find the perimeter. The perimeters of B and C were found by multiplying by 3/2 each time, because of the problem saying P(A) was 2/3 of P(B), and P(B) was 2/3 of P(C).