Question

In the above figure, if $AD = 2.0$ cm, $AE = 1.8$ cm, $EC = 3.6$ cm and $DE \parallel BC$ the measure of $BD$ will be : 

 

• A. 3.6 cm
• B. 4.0 cm
• C. 5.4 cm
• D. 6.0 cm

Hint:

Observe the scale: $EC$ is double $AE$ ($3.6 = 1.8 \times 2$), so $BD$ must be double $AD$ ($2.0 \times 2 = 4.0$).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
According to the Basic Proportionality Theorem (BPT) or Thales's Theorem, if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the other two sides in the same ratio.

Step 2: Setting up the Ratio:
Since $DE \parallel BC$:
$$\frac{AD}{BD} = \frac{AE}{EC}$$
Step 3: Calculation:
Substitute the given values:
$$\frac{2.0}{BD} = \frac{1.8}{3.6}$$
Since $1.8 / 3.6 = 1/2$:
$$\frac{2.0}{BD} = \frac{1}{2}$$
$$BD = 2.0 \times 2 = 4.0 \text{ cm}$$
Step 4: Final Answer:
The measure of $BD$ is 4.0 cm.