Question

The perimeter of the rectangle below is 46 units. Find the value of Z. Z=

Answer 1

The value of z is z = 5

To solve this, we need to create an equation. the perimeter of a rectangle is:

`P=2L+2l`

Where L is the lenght of the longer sides and l the lenght of the shorter sides.

Then we know by the picture that:

`\begin{gathered} L=3z-2 \\ l=2z \end{gathered}`

Replacing this values and the fact that the perimeter is 46 on the equation for the perimeter:

`P=2L+2l\Rightarrow46=2(3z-2)+2(2z)`

Now solve for z:

`\begin{gathered} 46=2\cdot3z+2(-2)+4z \\ 46=6z+4z-4 \\ 46+4=10z \\ 50=10z \\ (50)/(10)=z \\ z=5 \end{gathered}`