Question

Figure CDEF is a parallelogram.



What is the value of r?

2
3
4
5

Answer 1

Given that figure CDEF is a parallelogram.

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Using the property of a parallelogram which says that the length of any two opposite sides are equal. We have:

CF = DE
10r - 20 = 6r
10r - 6r = 20
4r = 20
r = 20 / 4
r = 5

Answer 2

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

$\rm CF =10r-20.....(1)\\DE = 6r........(2)\\CD = 2r+12 .........(3)$

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

$\rm CF = DE.........(4)$

From equations (1) ,(2) and (4) we can say that

$\rm 10r -20 =6r \\4r =20\\r =20/4= 5\\\bold {r=5 }$

The value of r is 5

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