Question:
A rectangular sheet of paper, when halved by folding it at the mid point of its longer side, results in a rectangle, whose longer and shorter sides are in the same proportion as the longer and shorter sides of the original rectangle. If the shorter side of the original rectangle is 2, what is the area of the smaller rectangle?
A rectangular sheet of paper, when halved by folding it at the mid point of its longer side, results in a rectangle, whose longer and shorter sides are in the same proportion as the longer and shorter sides of the original rectangle. If the shorter side of the original rectangle is 2, what is the area of the smaller rectangle?
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After folding, the new rectangle has sides \(L/2\) and the original shorter side. Set up the similarity of the two rectangles.
Updated On: Nov 4, 2026
- \(4\sqrt{2}\)
- \(2\sqrt{2}\)
- \(\sqrt{2}\)
- None of the above
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The Correct Option is B
Solution and Explanation
Step 1: Set up.
Let the original sides be \(L\) (longer) and \(2\) (shorter). Folding at the mid point of the longer side gives a rectangle with sides \(\frac{L}{2}\) and \(2\). Its longer side is 2 and its shorter side is \(\frac{L}{2}\).
Step 2: Similarity.
\(\dfrac{L}{2}=\dfrac{2}{L/2}\Rightarrow \dfrac{L}{2}=\dfrac{4}{L}\Rightarrow L^2=8\Rightarrow L=2\sqrt{2}\).
Step 3: Area of the smaller rectangle.
Area \(=\frac{L}{2}\times 2=\sqrt{2}\times 2=2\sqrt{2}\).
Final Answer:
The correct option is (2): \(2\sqrt{2}\)
Let the original sides be \(L\) (longer) and \(2\) (shorter). Folding at the mid point of the longer side gives a rectangle with sides \(\frac{L}{2}\) and \(2\). Its longer side is 2 and its shorter side is \(\frac{L}{2}\).
Step 2: Similarity.
\(\dfrac{L}{2}=\dfrac{2}{L/2}\Rightarrow \dfrac{L}{2}=\dfrac{4}{L}\Rightarrow L^2=8\Rightarrow L=2\sqrt{2}\).
Step 3: Area of the smaller rectangle.
Area \(=\frac{L}{2}\times 2=\sqrt{2}\times 2=2\sqrt{2}\).
Final Answer:
The correct option is (2): \(2\sqrt{2}\)
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