Question

El perimetro del cuadrado x es dos tercios del perimetro del cuadrado Y. El cuadrado y es dos tercios del perimetro del cuadrado Z. El area del cuadrado X es 16cm2 ?Cual es el area del cuadrado Z?

Answer 1

For this case we have that by definition, the perimeter of a square is given by
`P = 4l` and the area is given by
`A = l ^ 2 = l * l`

Where "l" represents the side of the square.

Be:

• Px: Perimeter of the square x

• Py: Perimeter of the square and

• Pz: Perimeter of square z

We have the following information:

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

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

`Ax = 16cm ^ 2`, which can be rewritten as
`Ax = 4cm * 4cm`, so, the side of the square x is
`lx = 4cm`

So, we can find the perimeter of x:

`Px = 4lx = 4 * 4cm = 16cm`

So, we know that
`Px =(2)/(3) Py`, then:

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

`Py =(3)/(2) * 16cm`

`Py = 24cm`

We know that
`Py =(2)/(3) Pz`, then:

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

`Pz =(3)/(2)*24cm`

`Pz = 36cm`

If the perimeter of the square z is 36 cm, then the side, lz, is given by:

`36cm = 4lz`

`lz =(36)/(4)`

`lz = 9cm`

Thus, the area of the square z is:

`Az = lz * lz\\Az = 9cm * 9cm\\Az = 81cm ^ 2`

Answer:

The area of the square z is
`Az = 81cm ^ 2`