Question:
It is given that $\Delta ABC \sim \Delta QRP$ such that $AB = 9$ cm, $BC = 5$ cm and $PR = 2$ cm. Length of side QR is :
It is given that $\Delta ABC \sim \Delta QRP$ such that $AB = 9$ cm, $BC = 5$ cm and $PR = 2$ cm. Length of side QR is :
Show Hint
Always pay close attention to the order of vertices in a similarity statement!
A common mistake is writing $\frac{AB}{PQ}$ or $\frac{AB}{QR}$ arbitrarily.
Write down the letters of the triangles vertically aligned to match them up:
A $\rightarrow$ Q
B $\rightarrow$ R
C $\rightarrow$ P
This ensures you write the ratios correctly: $AB$ corresponds to $QR$, and $BC$ corresponds to $RP$.
A common mistake is writing $\frac{AB}{PQ}$ or $\frac{AB}{QR}$ arbitrarily.
Write down the letters of the triangles vertically aligned to match them up:
A $\rightarrow$ Q
B $\rightarrow$ R
C $\rightarrow$ P
This ensures you write the ratios correctly: $AB$ corresponds to $QR$, and $BC$ corresponds to $RP$.
Updated On: Jul 7, 2026
- $0.9$ cm
- $\frac{5}{18}$ cm
- $\frac{10}{9}$ cm
- $3.6$ cm
Show Solution
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Question:
This question is based on the concept of "Similar Triangles".
We are given that triangle $ABC$ is similar to triangle $QRP$ ($\Delta ABC \sim \Delta QRP$).
We are given specific lengths of three sides: $AB = 9$ cm, $BC = 5$ cm, and $PR = 2$ cm.
We need to determine the length of the side $QR$.
Step 2: Key Formula or Approach:
The fundamental property of similar triangles states that if two triangles are similar, their corresponding angles are equal, and their corresponding sides are proportional.
For the similarity relation $\Delta ABC \sim \Delta QRP$, the corresponding sides must be matched in the exact order of the vertices:
\[ \frac{AB}{QR} = \frac{BC}{RP} = \frac{AC}{QP} \] We will select the appropriate pair of ratios that contain the given values and the unknown side $QR$.
Step 3: Detailed Explanation:
• Write down the similarity relationship given in the problem:
\[ \Delta ABC \sim \Delta QRP \]
• State the proportionality of corresponding sides:
\[ \frac{AB}{QR} = \frac{BC}{RP} \]
• Note the given values:
• $AB = 9$ cm
• $BC = 5$ cm
• $PR$ (which is the same as $RP$) $= 2$ cm
• Substitute these values into the proportionality equation:
\[ \frac{9}{QR} = \frac{5}{2} \]
• Solve the equation for $QR$ by cross-multiplication:
\[ 5 \cdot QR = 9 \cdot 2 \] \[ 5 \cdot QR = 18 \]
• Divide both sides by 5:
\[ QR = \frac{18}{5} = 3.6\text{ cm} \]
Step 4: Final Answer:
The length of the side $QR$ is $3.6$ cm, which corresponds to Option (D).
This question is based on the concept of "Similar Triangles".
We are given that triangle $ABC$ is similar to triangle $QRP$ ($\Delta ABC \sim \Delta QRP$).
We are given specific lengths of three sides: $AB = 9$ cm, $BC = 5$ cm, and $PR = 2$ cm.
We need to determine the length of the side $QR$.
Step 2: Key Formula or Approach:
The fundamental property of similar triangles states that if two triangles are similar, their corresponding angles are equal, and their corresponding sides are proportional.
For the similarity relation $\Delta ABC \sim \Delta QRP$, the corresponding sides must be matched in the exact order of the vertices:
\[ \frac{AB}{QR} = \frac{BC}{RP} = \frac{AC}{QP} \] We will select the appropriate pair of ratios that contain the given values and the unknown side $QR$.
Step 3: Detailed Explanation:
• Write down the similarity relationship given in the problem:
\[ \Delta ABC \sim \Delta QRP \]
• State the proportionality of corresponding sides:
\[ \frac{AB}{QR} = \frac{BC}{RP} \]
• Note the given values:
• $AB = 9$ cm
• $BC = 5$ cm
• $PR$ (which is the same as $RP$) $= 2$ cm
• Substitute these values into the proportionality equation:
\[ \frac{9}{QR} = \frac{5}{2} \]
• Solve the equation for $QR$ by cross-multiplication:
\[ 5 \cdot QR = 9 \cdot 2 \] \[ 5 \cdot QR = 18 \]
• Divide both sides by 5:
\[ QR = \frac{18}{5} = 3.6\text{ cm} \]
Step 4: Final Answer:
The length of the side $QR$ is $3.6$ cm, which corresponds to Option (D).
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