To solve the exercise, you can first draw a picture to better understand the statement. So,
Now, in a rectangle, the lengths of the diagonals measure the same. So,
[tex]\begin{gathered} WY=XZ \\ -2x+34=3x-26 \end{gathered}[/tex]
To solve for x first subtract 34 from both sides of the equation
[tex]\begin{gathered} -2x+34-34=3x-26-34 \\ -2x=3x-60 \end{gathered}[/tex]
Subtract 3x from both sides of the equation
[tex]\begin{gathered} -2x-3x=3x-60-3x \\ -5x=-60 \end{gathered}[/tex]
Divide by -5 into both sides of the equation
[tex]\begin{gathered} \frac{-5x}{-5}=\frac{-60}{-5} \\ x=12 \end{gathered}[/tex]
Finally, replace the value of x in the length of any of the diagonals, for example, the diagonal WY
[tex]\begin{gathered} WY=-2x+34 \\ WY=-2(12)+34 \\ WY=-24+34 \\ WY=10 \end{gathered}[/tex]
Therefore, the length of each diagonal is 10 units.
