Question

What is the value of r?



What is the length of segment EF?

Answer 1

9r-6=8r+3
9r=8r+9
r=9
EF=DC
EF=4(9)+19
EF=36+19
EF=55

Answer 2

Since we know that the opposite sides of parallelogram are congruent. We will use this property of parallelogram to answer our both problems.

We can see from our diagram that CDEF is a parallelogram.

1. Let us find value of r by equating opposite sides of our parallelogram to one another.

CF=ED

$9r-6=8r+3$

Upon combining like terms we will get,

$9r-8r=3+6$

$(9-8)r=9$

$r=9$

Therefore, we can see that r equals to 9.

2. Since we know that opposite sides of parallelogram are equal. We can find length of line segment EF by finding length of line segment CD.

We have been given that line segment CD equals to $4r+19$.

Let us substitute r=9 in this expression.

$CD=4\cdot 9+19$

$CD=36+19$

$CD=55$

Therefore, length of line segment EF is 55.