Question

Let AC = 16, AB = x + 1, and BC = x + 7. What is the measure of the length of AB?

Answer 1

Since the segments AB and BC are connected by the point B, the sum of their lengths is equal the length of segment AC.

So we have that:

$\begin{gathered} AB+BC=AC \\ x+1+x+7=16 \\ 2x+8=16 \\ 2x=16-8 \\ 2x=8 \\ x=\frac{8}{2} \\ x=4 \end{gathered}$

Calculating the length of AB:

$\begin{gathered} AB=x+1 \\ AB=4+1 \\ AB=5 \end{gathered}$