Question

EL PERIMETRO DELCUADRADO X ES DOS TERCIOS DEL PERIMETRO DEL CUADRADO Y. EL UCADRADO Y ES DOS TERCIOS DEL PERIMETRO DEL CUADRADO Z. EL AREA DEL CUADRADO X ES DE 16 CM2 ¿CUAL ES AREA DEL CUADRADO Z?

Answer 1

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

$Px=\frac{2}{3} Py$ -------> equation A

$Py=\frac{2}{3} Pz$ -------> equation B

$Ax=16\ cm^{2}$

$Ax=x^{2}$

so

$x^{2}=16$

$x=4\ cm$

Step 2

Find the perimeter of square x

$Px=4x$

substitute the value of x in the formula

$Px=4*4=16\ cm$

Step 3

Find the perimeter of square y

use the equation A

$Px=\frac{2}{3} Py$

solve for Py

$Py=\frac{3}{2} Px$

substitute the value of Px

$Py=\frac{3}{2}16=24\ cm$

Step 4

Find the perimeter of square z

use the equation B

$Py=\frac{2}{3} Pz$

solve for Pz

$Pz=\frac{3}{2} Py$

substitute the value of Py

$Pz=\frac{3}{2} 24=36\ cm$

Step 5

Find the area of square z

we know that

the area of the square z is equal to

$Az=z^{2}$

Find the length side of square z

$Pz=4z$

$Pz=36\ cm$

so

$4z=36$

$z=9\ cm$

substitute the value of z in the area's formula

$Az=9^{2}=81\ cm^{2}$

therefore

the answer is

the area of the square z is $81\ cm^{2}$