Question

If \(\Delta DEF \sim \Delta PQR\) such that \(3 DE = PQ\) and \(EF = 6\) cm, then the length of QR is :

• A. 12 cm
• B. 3 cm
• C. 2 cm
• D. 18 cm

Hint:

Double check the correspondence order of vertices in similarity statements.
Here, \(\Delta DEF \sim \Delta PQR\) implies \(DE\) corresponds to \(PQ\) and \(EF\) corresponds to \(QR\).

Answer 1

The Correct Option is D

Step 1: Find the scale factor between the two triangles.
Since $3\,DE = PQ$, the scale factor from $\Delta DEF$ to $\Delta PQR$ is $k = \frac{PQ}{DE} = 3$.
Step 2: Apply the same scale factor to every side.
Because the triangles are similar, every side of $\Delta PQR$ is exactly $k$ times the corresponding side of $\Delta DEF$, so $QR = k \times EF$.
Step 3: Compute QR.
\[ QR = 3 \times 6 \]
\[ \boxed{18 \text{ cm}} \]