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A rectangular sheet of paper, when halved by folding it at the mid

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A rectangular sheet of paper, when halved by folding it at the mid  [#permalink]

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New post 25 Oct 2018, 04:50
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Question Stats:

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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. \(4 \sqrt{2}\)
b. \(2 \sqrt{2}\)
c. \(\sqrt{2}\)
d. 1
e. 3
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A rectangular sheet of paper, when halved by folding it at the mid  [#permalink]

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New post 25 Oct 2018, 06:02
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RhythmGMAT wrote:
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. \(4 \sqrt{2}\)
b. \(2 \sqrt{2}\)
c. \(\sqrt{2}\)
d. 1
e. 3


\(\frac{l}{b} = \frac{b}{(l/2)}\) where \(b = 2\) given

i.e. \(b^2 = l^2 / 2\)

i.e. \(l = 2√2\)

Area of smaller rectangle \(= (l/2)*b = (2√2/2)*2 = 2√2\)

Answer: Option B
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Re: A rectangular sheet of paper, when halved by folding it at the mid  [#permalink]

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New post 25 Oct 2018, 07:05
2
RhythmGMAT wrote:
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. \(4 \sqrt{2}\)
b. \(2 \sqrt{2}\)
c. \(\sqrt{2}\)
d. 1
e. 3


OA: B

Initial Rectangle Dimensions
longer side \(= x\)
Shorter side\(= 2\)

Dimensions after folding
Longer side \(= 2\)
Shorter side \(= \frac{x}{2}\)

As per question
\(\frac{x}{2}=\frac{2}{\frac{x}{2}}\)
\(x^2=8 \quad;\quad x=2\sqrt{2}\)

Dimensions of Shorter Rectangle
Longer side \(= 2\)
Shorter side \(=\frac{2\sqrt{2}}{2}=\sqrt{2}\)
Area of Shorter Rectangle \(= 2\sqrt{2}\)
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Re: A rectangular sheet of paper, when halved by folding it at the mid  [#permalink]

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New post 25 Oct 2018, 14:13
2
RhythmGMAT wrote:
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. \(4 \sqrt{2}\)
b. \(2 \sqrt{2}\)
c. \(\sqrt{2}\)
d. 1
e. 3

\(?\,\, = 2x\)

Image


The rectangles shown above are similar, hence:

\({{2x} \over 2} = {2 \over x}\,\,\,\,\, \Rightarrow \,\,\,{x^2} = 2\,\,\,\,\,\mathop \Rightarrow \limits^{x\,\, > \,\,0} \,\,\,\,x = \sqrt 2 \,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 2\sqrt 2\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: A rectangular sheet of paper, when halved by folding it at the mid &nbs [#permalink] 25 Oct 2018, 14:13
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