Question

In the figure $DE \parallel BC$. If $AD = 3\,\text{cm}$, $DE = 4\,\text{cm}$ and $DB = 1.5\,\text{cm}$, then the measure of $BC$ will be:

• A. $9\,\text{cm}$
• B. $8\,\text{cm}$
• C. $7.5\,\text{cm}$
• D. $6\,\text{cm}$

Hint:

When a line parallel to the base cuts the other two sides of a triangle, use $\frac{\text{segment on the smaller triangle}}{\text{corresponding side of the big triangle}}=\frac{\text{adjacent side}}{\text{whole side}}$ to relate lengths quickly.

Answer 1

The Correct Option is D

Step 1: Use similarity in the triangle
Since $DE \parallel BC$, triangles $\triangle ADE$ and $\triangle ABC$ are similar. Hence the corresponding sides are proportional:
\[ \frac{DE}{BC}=\frac{AD}{AB}. \]

Step 2: Compute $AB$ and substitute
Given $AD=3\,\text{cm}$ and $DB=1.5\,\text{cm}$, so
\[ AB=AD+DB=3+1.5=4.5\,\text{cm}. \] Also $DE=4\,\text{cm}$. Using the ratio:
\[ \frac{4}{BC}=\frac{3}{4.5}\Rightarrow BC=\frac{4\times 4.5}{3}=4\times 1.5=6\,\text{cm}. \]

Step 3: Conclusion
Therefore, the length of $BC$ is $6\,\text{cm}$.
The correct answer is option (D).