The calcuuated length of the segment AC is
![12 (23)/(56) \text{ units}](https://img.qammunity.org/2022/formulas/mathematics/high-school/gs67wpe73tky3f8kof3sp6k8jk8g2t7di4.png)
How to determine the length of the segment AC
From the question, we have the following parameters that can be used in our computation:
![\text{AB} = 7 \frac18 \text{units}](https://img.qammunity.org/2022/formulas/mathematics/high-school/jdayv9nppv6f4djo5j1cnjjrvs6xxgp45a.png)
![\text{BC} = 5 \frac27 \text{units}](https://img.qammunity.org/2022/formulas/mathematics/high-school/gj4gmdfnco4l1ny126db8u0s86jp0iaerm.png)
Using the above as a guide, we have the following:
AC = AB + BC
Substitute the known values into the equation
![\text{Length AC} = 7\frac18 \text{ units} + 5 \frac27 \text{ units}](https://img.qammunity.org/2022/formulas/mathematics/high-school/qd9kn07ezmq60fwo1pygdvae9ytqn9nre8.png)
Evaluate the sum of the integers
![\text{Length AC} = 12 + \frac18 \text{ units} + \frac27 \text{ units}](https://img.qammunity.org/2022/formulas/mathematics/high-school/laz4um34rm33ufwj4cx14eq7aq4anuizom.png)
Take the LCM and add the fractions
This gives
![\text{Length AC} = 12 (23)/(56) \text{ units}](https://img.qammunity.org/2022/formulas/mathematics/high-school/q71d1wd3j879bgpfbovvamw5l5a8ng9syz.png)
Hence, the length of the segment AC is
![12 (23)/(56) \text{ units}](https://img.qammunity.org/2022/formulas/mathematics/high-school/gs67wpe73tky3f8kof3sp6k8jk8g2t7di4.png)