The value of r is 5
A parallelogram is a quadrilateral with parallel opposite sides but the angle between adjacent side is not 90°. Two opposite angles are equal and acute in nature and the other two opposite angles are equal and obtuse in nature.
Given CDEF is a parallelogram
![\rm CF =10r-20.....(1)\\DE = 6r........(2)\\CD = 2r+12 .........(3)](/tpl/images/0475/8189/bf4ef.png)
We have to find out the value of r
According to the property of parallelogram
The opposite sides of parallelogram are equal and hence we can right
![\rm CF = DE.........(4)](/tpl/images/0475/8189/546d5.png)
From equations (1) ,(2) and (4) we can say that
![\rm 10r -20 =6r \\4r =20\\r =20/4= 5\\\bold {r=5 }](/tpl/images/0475/8189/50d8f.png)
The value of r is 5
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