Question

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

Answer 1

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