Answer:
11 units
Explanation:
Given that lines EB and DC are parallel, we use the proportional division theorem:
[tex]\frac{AE}{ED}=\frac{AB}{BC}[/tex]
Substitute the given values:
[tex]\begin{gathered} \frac{2}{ED}=\frac{10}{45} \\ \text{Cross multiply} \\ ED\times10=2\times45 \\ \text{Divide both sides by 10} \\ \frac{ED\times10}{10}=\frac{2\times45}{10} \\ ED=9 \end{gathered}[/tex]
Next, find the length of AD:
[tex]\begin{gathered} AD=AE+ED \\ =2+9 \\ =11\text{ units} \end{gathered}[/tex]
The length of AD is 11 units.
Alternate Method
[tex]ED=AD-2[/tex]
So, we have that:
[tex]\frac{AE}{ED}=\frac{AB}{BC}\implies\frac{AE}{AD-2}=\frac{AB}{BC}[/tex]
Substitute the given values:
[tex]\frac{2}{AD-2}=\frac{10}{45}[/tex]
Cross multiply:
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