Question

nearest tenth if necessary.
answer attempt 1 out of 4
x =

Explanation:

Step1: Use the basic proportionality theorem (Thales' theorem)

If a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides those sides proportionally. So, \(\frac{CD}{DA}=\frac{CE}{EB}\).

Step2: Substitute the given values

We know \(CD = 5.1\), \(DA=6.9\), \(EB = 5.1\) and \(CE=x\). Substituting into \(\frac{CD}{DA}=\frac{CE}{EB}\), we get \(\frac{5.1}{6.9}=\frac{x}{5.1}\).

Step3: Solve for \(x\)

Cross - multiply: \(6.9x=5.1\times5.1\). Then \(x=\frac{5.1\times5.1}{6.9}\). Calculate \(5.1\times5.1 = 26.01\), so \(x=\frac{26.01}{6.9}\approx3.8\).

Answer:

\(3.8\)