Answer:
18.1cm
Step-by-step explanation:
Please refer to the attached photo for a better understanding. Apologies for the terrible drawing.
First we will find the length of BE by using pythagoras' Theorem.
[tex]c^{2} =a^{2} +b^{2} \\AB^{2} =BE^{2} +EA^{2} \\16^{2} =BE^{2} +7^{2} \\256=BE^{2} +49\\BE^{2} =256-49\\BE=\sqrt{207} cm[/tex]
We will leave BE as it is as it is not the final answer.
Since we know CD = BE,
CD = [tex]\sqrt{207} cm[/tex]
Now from the photo, draw a line from C to A or A to C, you will see another triangle.
Now we will use Pythagora's Theorem again to find AC.
[tex]AC^{2} =AD^{2} +DC^{2} \\AC^{2} =11^{2} +(\sqrt{207}) ^{2} \\AC^{2} = 121+207\\AC^{2} =328\\AC=\sqrt{328} \\=18.1cm (1dp)[/tex]
