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Find the lengths of the diagonals of rectangle WXY Z where WY-2x + 34 and XZ = 3x – 26The length of each diagonal isunits.

Find The Lengths Of The Diagonals Of Rectangle WXY Z Where WY2x 34 And XZ 3x 26The Length Of Each Diagonal Isunits class=

Sagot :

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.

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