Question:
If \(\Delta DEF \sim \Delta PQR\) such that \(3 DE = PQ\) and \(EF = 6\) cm, then the length of QR is :
If \(\Delta DEF \sim \Delta PQR\) such that \(3 DE = PQ\) and \(EF = 6\) cm, then the length of QR is :
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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 \(QR\).
Here, \(\Delta DEF \sim \Delta PQR\) implies \(DE\) corresponds to \(PQ\) and \(EF\) corresponds to \(QR\).
Updated On: Jul 9, 2026
- 12 cm
- 3 cm
- 2 cm
- 18 cm
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Question:
We are given two similar triangles, \(\Delta DEF\) and \(\Delta PQR\). We are given a relationship between their corresponding sides \(DE\) and \(PQ\), and the length of side \(EF\). We need to determine the length of corresponding side \(QR\).
Step 2: Key Formula or Approach:
If two triangles are similar, the ratios of their corresponding sides are equal:
\[ \frac{DE}{PQ} = \frac{EF}{QR} = \frac{DF}{PR} \]
Step 3: Detailed Explanation:
• Write down the given relationship:
\[ 3 DE = PQ \implies \frac{DE}{PQ} = \frac{1}{3} \]
• Set up the ratio for the corresponding sides:
\[ \frac{DE}{PQ} = \frac{EF}{QR} \]
• Substitute the known values (\(\frac{DE}{PQ} = \frac{1}{3}\) and \(EF = 6\)):
\[ \frac{1}{3} = \frac{6}{QR} \]
• Solve for \(QR\):
\[ QR = 6 \times 3 = 18 \text{ cm} \]
Step 4: Final Answer:
The length of \(QR\) is 18 cm.
We are given two similar triangles, \(\Delta DEF\) and \(\Delta PQR\). We are given a relationship between their corresponding sides \(DE\) and \(PQ\), and the length of side \(EF\). We need to determine the length of corresponding side \(QR\).
Step 2: Key Formula or Approach:
If two triangles are similar, the ratios of their corresponding sides are equal:
\[ \frac{DE}{PQ} = \frac{EF}{QR} = \frac{DF}{PR} \]
Step 3: Detailed Explanation:
• Write down the given relationship:
\[ 3 DE = PQ \implies \frac{DE}{PQ} = \frac{1}{3} \]
• Set up the ratio for the corresponding sides:
\[ \frac{DE}{PQ} = \frac{EF}{QR} \]
• Substitute the known values (\(\frac{DE}{PQ} = \frac{1}{3}\) and \(EF = 6\)):
\[ \frac{1}{3} = \frac{6}{QR} \]
• Solve for \(QR\):
\[ QR = 6 \times 3 = 18 \text{ cm} \]
Step 4: Final Answer:
The length of \(QR\) is 18 cm.
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