Question

identifying a side length
what is the value of r?
what is the length of segment ef?
units
9
55
75
130

Explanation:

Step1: Set equal sides

Assume the two - marked equal sides give the equation $9r - 6=4r + 19$.

Step2: Solve for $r$

Subtract $4r$ from both sides: $9r-4r - 6=4r-4r + 19$, which simplifies to $5r-6 = 19$. Then add 6 to both sides: $5r-6 + 6=19 + 6$, so $5r=25$. Divide both sides by 5: $r=\frac{25}{5}=5$.

Step3: Find length of EF

The length of EF is given by $8r + 3$. Substitute $r = 5$ into the expression: $8\times5+3=40 + 3=43$. But since it seems there are multiple - choice options for the length of EF and we made an assumption about the equal - side relationship (if we assume the correct equal - side relationship based on the markings), if we assume $9r-6=8r + 3$

Step1: Solve for $r$

Subtract $8r$ from both sides: $9r-8r-6=8r-8r + 3$, so $r-6=3$. Add 6 to both sides: $r=9$.

Step2: Find length of EF

Substitute $r = 9$ into the expression for EF ($8r + 3$). Then $8\times9+3=72 + 3=75$.

Answer:

What is the value of $r$? 9
What is the length of segment EF? 75 units