Question

Find the values of the variables for the parallelogram if m<1=3y-9. Round your answers to two decimal places if necessary!

Answer 1

Notice that the parallelogram has 2 equal sides and one right angle, therefore, the parallelogram is a square.

Then, we have that the diagonals are perpendicular, which gives us the following equation:

`3y-9=90`

solving for y we get:

`\begin{gathered} 3y-9=90 \\ \Rightarrow3y=90+9=99 \\ \Rightarrow y=(99)/(3)=33 \\ y=33 \end{gathered}`

we also have that each diagonal bisect the angles of the square. Since all the angles are right angles, we have for x and z:

`\begin{gathered} 5x=45\Rightarrow x=(45)/(5)=9 \\ 10z=45\Rightarrow z=(45)/(10)=(9)/(2) \end{gathered}`

therefore, y = 33, x = 9 and z = 9/2