Question

using the side - splitter theorem, daniel wrote a proportion for the segments formed by line segment de. what is ec?
there is a triangle abc, with d on ab and e on bc. the length of ad is 3, db is 5, be is 4, and ec is unknown (marked as ?). the proportion given is \\(\frac{ad}{db}=\frac{ec}{be}\\) and then \\(\frac{3}{5}=\frac{ec}{4}\\). the options are 3 units, 2.4 units, 2 units, 3.75 units.

Explanation:

Step1: Identify the proportion

From the side - splitter theorem, we have the proportion \(\frac{AD}{DB}=\frac{EC}{BE}\). We know that \(AD = 3\), \(DB=5\), and \(BE = 4\). Let \(EC=x\). So the proportion becomes \(\frac{3}{5}=\frac{x}{4}\).

Step2: Solve for \(x\)

Cross - multiply the proportion \(\frac{3}{5}=\frac{x}{4}\). Cross - multiplying gives us \(5x=3\times4\), which simplifies to \(5x = 12\). Then, divide both sides by 5: \(x=\frac{12}{5}=2.4\).

Answer:

2.4 units