Question

identifying a side length
what is the value of r?
what is the length of segment ef?
units
4r + 19
9r - 6
8r + 3

Explanation:

Step1: Set equal congruent sides

$9r - 6 = 8r + 3$

Step2: Solve for $r$

$9r - 8r = 3 + 6$
$r = 9$

Step3: Substitute $r$ into EF's expression

$EF = 4r + 19 = 4(9) + 19$

Step4: Calculate EF's length

$EF = 36 + 19 = 55$

Answer:

The value of $r$ is 9.
The length of segment EF is 55 units.