Chapter 3, Problem 6CR

To determine

To calculate: Measure of AC

Answer to Problem 6CR

The Measure of AC is $41\text{ units}$ .

Explanation of Solution

Given information : Here, we have given that AB = $2r+7$ , CD = $3r-1$ , BC = $6$ and C is the midpoint of $\overline{AD}$ .

Formula used: $AB+BC=AC$

Calculation: $AC=AB+BC$

  $\begin{array}{l}\Rightarrow AC=2r+7+6\\ \Rightarrow AC=2r+13\end{array}$

As, C is the midpoint of $\overline{AD}$ .

  $\begin{array}{l}\Rightarrow AC=CD\\ \Rightarrow 2r+13=3r-1\\ \Rightarrow 13+1=3r-2r\\ \Rightarrow 14=r\end{array}$

Or $r=14$

Now, put value of $r=14$ in $AC=2r+13$

  $\begin{array}{l}\Rightarrow AC=2r+13\\ \Rightarrow AC=2(14)+13\\ \Rightarrow AC=28+13\\ \Rightarrow AC=41\text{ units}\end{array}$