Question

What is the length of AB BC And AC in inches

Answer 1

Since ∠A and ∠C are congruent, it follows that the sides opposite to these angles are also congruent.

`\begin{gathered} \overline{AB}=\overline{BC} \\ \\ \text{Substitute the following sides using their given} \\ 5x-3=3x+7 \\ 5x-3=3x+7 \\ 5x-3x=7+3 \\ 2x=10 \\ \frac{\cancel{2}x}{\cancel{2}}=(10)/(2) \\ x=5 \end{gathered}`

Now that we know the value of x, substitute this to AB and we get

`\begin{gathered} \overline{AB}=5x-3 \\ \overline{AB}=5(2)-3 \\ \overline{AB}=10-3 \\ \overline{AB}=7\text{ inches} \end{gathered}`

Therefore, the length of AB is 7 inches.

`\begin{gathered} \overline{AC}=6x-3 \\ \overline{AC}=6(2)-3 \\ \overline{AC}=12-3 \\ \overline{AC}=9\text{ inches.} \\ \\ \overline{BC}=3x+7 \\ \overline{BC}=3(2)+7 \\ \overline{BC}=6+7 \\ \overline{BC}=13\text{ inches} \end{gathered}`