Question

In the given figure \(\triangle\)ABC is shown, in which DE \(\parallel\) BC. If AD = 5 cm, DB = 2.5 cm and DE = 8 cm, then the length of BC is :

• A. 10 cm
• B. 6 cm
• C. 12 cm
• D. 7.5 cm

Hint:

Avoid using \( \frac{AD}{DB} = \frac{DE}{BC} \). This is a common mistake. BPT relates segments of sides, but Similarity relates the full sides of the triangles.

Answer 1

The Correct Option is C

To solve the given problem, we will use the Basic Proportionality Theorem (Thales' Theorem), which states that if a line is drawn parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.

Given:

• \(DE \parallel BC\)
• \(AD = 5\, \text{cm}\)
• \(DB = 2.5\, \text{cm}\)
• \(DE = 8\, \text{cm}\)

To find: Length of \(BC\)

According to the Basic Proportionality Theorem:

\(\frac{AD}{DB} = \frac{DE}{BC}\)

Substituting the given values:

\(\frac{5}{2.5} = \frac{8}{BC}\)

Solving for \(BC\):

\(\frac{5}{2.5} = 2 \Rightarrow \frac{8}{BC} = 2\)

From the above equation, we have:

\(BC = \frac{8}{2} = 4 \times 3 = 12\, \text{cm}\)

Thus, the length of \(BC\) is 12 cm.