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

To solve for the measure of \( BD \), we need to use the Basic Proportionality Theorem (also known as Thales' theorem). According to this theorem, if a line is drawn parallel to one side of a triangle, then it divides the other two sides proportionally.

Given:

• \( AD = 2.0 \, \text{cm} \)
• \( AE = 1.8 \, \text{cm} \)
• \( EC = 3.6 \, \text{cm} \)
• \( DE \parallel BC \)

By the Basic Proportionality Theorem, \( \frac{AD}{DB} = \frac{AE}{EC} \).

Let's denote \( DB = x \). Therefore,

\(\frac{2.0}{x} = \frac{1.8}{3.6}\)

Solving the proportion, we have:

\(\frac{2}{x} = \frac{1}{2}\)

This implies:

\(x = 4.0 \, \text{cm}\)

Therefore, the measure of \( BD \) is 4.0 cm.

Thus, the correct answer is 4.0 cm.