Question

A is the midpoint of BC. If AB = 4x - 7 and AC = 2x + 9, then find BC.

Answer 1

If A is the midpoint of BC, AB is equal to AC, so:

AB = AC

4x - 7 = 2x + 9

Solving for x, we get:

$\begin{gathered} 4x-7=2x+9 \\ 4x-7-2x=2x+9-2x \\ 2x-7=9 \\ 2x-7+7=9+7 \\ 2x=16 \\ \frac{2x}{2}=\frac{16}{2} \\ x=8 \end{gathered}$

On the other hand, BC is equal to the sum of AB and AC, so:

BC = AB + AC

BC = (4x - 7) + (2x + 9)

So, replacing x by 8, we get:

BC = (4*8 - 7) + (2*8 + 9)

BC = 25 + 25

BC = 50

Answer: BC = 50