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=(2)/(3) Py` -------> equation A

`Py=(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=(2)/(3) Py`

solve for Py

`Py=(3)/(2) Px`

substitute the value of Px

`Py=(3)/(2)16=24\ cm`

Step 4

Find the perimeter of square z

use the equation B

`Py=(2)/(3) Pz`

solve for Pz

`Pz=(3)/(2) Py`

substitute the value of Py

`Pz=(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)`