Question:
If rectangle \(ABCD\) has a perimeter of 68, and the longer edge is 2.4 times longer than the shorter edge, then how long is the diagonal \(AC\)?
If rectangle \(ABCD\) has a perimeter of 68, and the longer edge is 2.4 times longer than the shorter edge, then how long is the diagonal \(AC\)?
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Always express one side in terms of the other, use perimeter to find exact values, then apply Pythagoras for diagonals.
Updated On: Oct 3, 2025
- 26
- 32
- 30
- 24
- 13
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The Correct Option is B
Solution and Explanation
Step 1: Let shorter side = \(x\).
Then longer side = \(2.4x\). Step 2: Use perimeter.
\[ 2(x + 2.4x) = 68 \quad \Rightarrow \quad 2(3.4x) = 68 \quad \Rightarrow \quad x = 10 \] So shorter side = 10, longer side = 24. Step 3: Diagonal using Pythagoras.
\[ AC = \sqrt{10^2 + 24^2} = \sqrt{100 + 576} = \sqrt{676} = 26 \] Wait — correction. That matches option (1). Check carefully: If perimeter = 68, then \[ x + 2.4x = 34 \quad \Rightarrow \quad 3.4x = 34 \quad \Rightarrow \quad x=10 \] So diagonal is indeed 26.
Final Answer: \[ \boxed{26} \]
Then longer side = \(2.4x\). Step 2: Use perimeter.
\[ 2(x + 2.4x) = 68 \quad \Rightarrow \quad 2(3.4x) = 68 \quad \Rightarrow \quad x = 10 \] So shorter side = 10, longer side = 24. Step 3: Diagonal using Pythagoras.
\[ AC = \sqrt{10^2 + 24^2} = \sqrt{100 + 576} = \sqrt{676} = 26 \] Wait — correction. That matches option (1). Check carefully: If perimeter = 68, then \[ x + 2.4x = 34 \quad \Rightarrow \quad 3.4x = 34 \quad \Rightarrow \quad x=10 \] So diagonal is indeed 26.
Final Answer: \[ \boxed{26} \]
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