Question

segment am is the perpendicular bisector of segment bc. bm = 15z + 10, cm = 21z + 7. what is the length of segment bc?

Explanation:

Step1: Use property of perpendicular bisector

Since $AM$ is the perpendicular bisector of $BC$, then $BM = CM$. So we set up the equation $15z + 10=21z + 7$.

Step2: Solve the equation for $z$

Subtract $15z$ from both sides: $10 = 6z+7$. Then subtract 7 from both sides: $3 = 6z$. Divide both sides by 6, we get $z=\frac{3}{6}=\frac{1}{2}$.

Step3: Find the length of $BM$ or $CM$

Substitute $z = \frac{1}{2}$ into the expression for $BM$. $BM=15\times\frac{1}{2}+ 10=\frac{15}{2}+10=\frac{15 + 20}{2}=\frac{35}{2}$.

Step4: Calculate the length of $BC$

Since $BC = 2BM$ (because $M$ is the mid - point of $BC$), then $BC = 2\times\frac{35}{2}=35$.

Answer:

35