the question in English is
THE SQUARE PERIMETER X IS TWO THIRDS OF THE SQUARE PERIMETER Y. THE PERIMETER OF THE SQUARE Y IS TWO THIRDS OF THE PERIMETER OF THE SQUARE Z. THE AREA OF THE SQUARE X IS 16 CM2 WHAT IS THE AREA OF THE SQUARE Z?
Let
Px--------> the perimeter of square x
Py--------> the perimeter of square y
Pz--------> the perimeter of square z
Ax--------> the area of square x
Az--------> the area of square z
Step 1
Find the length side of the square x
we know that
[tex]Px=\frac{2}{3} Py[/tex] -------> equation A
[tex]Py=\frac{2}{3} Pz[/tex] -------> equation B
[tex]Ax=16\ cm^{2}[/tex]
[tex]Ax=x^{2}[/tex]
so
[tex]x^{2}=16[/tex]
[tex]x=4\ cm[/tex]
Step 2
Find the perimeter of square x
[tex]Px=4x[/tex]
substitute the value of x in the formula
[tex]Px=4*4=16\ cm[/tex]
Step 3
Find the perimeter of square y
use the equation A
[tex]Px=\frac{2}{3} Py[/tex]
solve for Py
[tex]Py=\frac{3}{2} Px[/tex]
substitute the value of Px
[tex]Py=\frac{3}{2}16=24\ cm[/tex]
Step 4
Find the perimeter of square z
use the equation B
[tex]Py=\frac{2}{3} Pz[/tex]
solve for Pz
[tex]Pz=\frac{3}{2} Py[/tex]
substitute the value of Py
[tex]Pz=\frac{3}{2} 24=36\ cm[/tex]
Step 5
Find the area of square z
we know that
the area of the square z is equal to
[tex]Az=z^{2}[/tex]
Find the length side of square z
[tex]Pz=4z[/tex]
[tex]Pz=36\ cm[/tex]
so
[tex]4z=36[/tex]
[tex]z=9\ cm[/tex]
substitute the value of z in the area's formula
[tex]Az=9^{2}=81\ cm^{2}[/tex]
therefore
the answer is
the area of the square z is [tex]81\ cm^{2}[/tex]
