For this case we have that by definition, the perimeter of a square is given by [tex]P = 4l[/tex] and the area is given by [tex]A = l ^ 2 = l * l[/tex]
Where "l" represents the side of the square.
Be:
We have the following information:
[tex]Px =\frac{2}{3}Py[/tex]
[tex]Py =\frac{2}{3}Pz[/tex]
[tex]Ax = 16cm ^ 2[/tex], which can be rewritten as [tex]Ax = 4cm * 4cm[/tex], so, the side of the square x is[tex]lx = 4cm[/tex]
So, we can find the perimeter of x:
[tex]Px = 4lx = 4 * 4cm = 16cm[/tex]
So, we know that [tex]Px =\frac{2}{3} Py[/tex], then:
[tex]Py =\frac{3}{2}Px[/tex]
[tex]Py =\frac{3}{2} * 16cm[/tex]
[tex]Py = 24cm[/tex]
We know that [tex]Py =\frac{2}{3} Pz[/tex], then:
[tex]Pz =\frac{3}{2} Py[/tex]
[tex]Pz =\frac{3}{2}*24cm[/tex]
[tex]Pz = 36cm[/tex]
If the perimeter of the square z is 36 cm, then the side, lz, is given by:
[tex]36cm = 4lz[/tex]
[tex]lz =\frac{36}{4}[/tex]
[tex]lz = 9cm[/tex]
Thus, the area of the square z is:
[tex]Az = lz * lz\\Az = 9cm * 9cm\\Az = 81cm ^ 2[/tex]
Answer:
The area of the square z is [tex]Az = 81cm ^ 2[/tex]
