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The perimeter of parallelogram WXYZ is 50 millimeters. What is WZ?

The perimeter of parallelogram WXYZ is 50 millimeters. What is WZ?-example-1

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Solution!!

The perimeter of parallelogram WXYZ is 50 millimeters.

Perimeter of the Parallelogram is equal to the Sum of allsides

WX + XY + YX + WZ

From the given figure,

WX = (2x + 9) mm

XY = (x - 5) mm

Since we know that opposite sides of Parallelogram are equal.

WX = YZ

WZ = XY

Plugging in the values,


\rm WX + XY + YX + WZ = 50


\rm (2x + 9) + (x - 5) + (2x + 9) + (x - 5) = 50

Opening the brackets,


\rm 2x + 9 + x - 5 + 2x + 9 + x - 5 = 50

Combining the like terms,


\rm 2x + x + 2x + x + 9 - 5 + 9 - 5 = 50


\rm 6x + 4 + 9 - 5 = 50


\rm 6x + 13 - 5 = 50


\rm 6x + 8 = 50

Subtract 8 from both sides,


\rm 6x + 8 - 8 = 50 - 8


\rm 6x = 42

Divide both sides by 6,


\rm x = 7

Since, WZ = (x - 5)


\rm 7 - 5 = 2 \: mm

Hence The value of WZ is 2 mm

User Beerbajay
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