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In the diagram of △△ADC below, EB∥∥DC, AE=2, AB=10, and BC=45. What is the length of AD?

In the diagram of △△ADC below, EB∥∥DC, AE=2, AB=10, and BC=45. What is the length-example-1
User Denmch
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1 Answer

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Answer:

11 units

Step-by-step explanation:

Given that lines EB and DC are parallel, we use the proportional division theorem:


(AE)/(ED)=(AB)/(BC)

Substitute the given values:


\begin{gathered} (2)/(ED)=(10)/(45) \\ \text{Cross multiply} \\ ED*10=2*45 \\ \text{Divide both sides by 10} \\ (ED*10)/(10)=(2*45)/(10) \\ ED=9 \end{gathered}

Next, find the length of AD:


\begin{gathered} AD=AE+ED \\ =2+9 \\ =11\text{ units} \end{gathered}

The length of AD is 11 units.

Alternate Method


ED=AD-2

So, we have that:


(AE)/(ED)=(AB)/(BC)\implies(AE)/(AD-2)=(AB)/(BC)

Substitute the given values:


(2)/(AD-2)=(10)/(45)

Cross multiply:


undefined

User Zookey
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