Question

In the figure, if \(DE \parallel BC\), then the measure of \(CE\) will be: 

• A. 5.5 cm
• B. 5.0 cm
• C. 4.8 cm
• D. 4.5 cm

Hint:

Use the Basic Proportionality Theorem whenever a line parallel to one side of a triangle divides the other two sides proportionally.

Answer 1

The Correct Option is B

Step 1: Recall the Basic Proportionality Theorem (Thales’ theorem).
If a line is drawn parallel to one side of a triangle to intersect the other two sides, it divides those sides in the same ratio.
Thus, \[ \dfrac{AD}{DB} = \dfrac{AE}{EC} \] Step 2: Substitute the given values.
From the figure, \[ AD = 1.3 \text{ cm}, \quad DB = 3.9 \text{ cm}, \quad AE = 1.5 \text{ cm} \] Let \(EC = x\). Then, \[ \dfrac{1.3}{3.9} = \dfrac{1.5}{x} \] Step 3: Simplify to find \(x\).
\[ x = \dfrac{1.5 \times 3.9}{1.3} = \dfrac{5.85}{1.3} \approx 4.5 \text{ cm} \] Step 4: Conclusion.
Therefore, the measure of \(CE\) is approximately \(4.5 \, \text{cm}\).