Mind Warmups-4

Algebra Level 2

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?

4√2 3√2 None of these √2

1 solution

Sandeep Bhardwaj
Aug 21, 2014

let larger side of original rectangle = $x.$

therefore according to given condition ,

$\frac{4}{x} = \frac{x}{2}$

$\implies x=2.\sqrt{2}$ .

So area of smaller rectangle $=2.\frac{x}{2}$

$=\boxed{ 2.\sqrt{2} .}$

This is the property the casual A3, A4, etc. papers have - the ratio of the longer side to the shorter side is always $\sqrt{2}$ , and an A4 sheet of paper can be created by cutting the A3 paper in half (by cutting through the midpoint of the longer side), and similarly with the other A's

mathh mathh - 6 years, 9 months ago

Mind Warmups-4

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