Question

The following figure is a rhombus. Find the value of m. Then, use that value to find the measure of VW

Answer 1

• 
  `m=8`

• The length of VW = 36 units.

Explanation:

We know that a rhombus is a quadrilateral with four sides. All four sides have the same length.

From the diagram, it is clear that

• The length of VW= 6m-12

• The length of WX = 4m+4

As all the four sides of the rhombus have equal length.

So we can observe

`VW=WX`

`6m-12 = 4m+4`

Add 12 to both sides

`6m-12+12=4m+4+12`

`6m=4m+16`

`2m=16`

Divide both sides by 2

`(2m)/(2)=(16)/(2)`

`m=8`

so

The length of VW= 6m-12

= 6(8)-12 ∵
`m=8`

= 48-12

= 36

Thereofore, the length of VW = 36 units.