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CAT 2004 — QA Question 16

Basics of Mensuration/PrismEasy

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?

Answer & solution

  • A

    4√2

  • 2√2

  • C

    √2

  • D

    None of the above

Solution

Let the length and breadth of the rectangle be x and y respectively.

x > y

By conditions, xy=yx2

∴  x22=y2

∴  x22 = 4 (∵ y = 2)

∴ x2 = 8

∴ x = 2√2

∴ Area of the smaller rectangle = 2√2 sq.units.

Hence, option (b).

CAT 2004 QA Q16: A rectangular sheet of paper, when halved by folding it at the mid-point of its longer side, results in a rect — Solution | TheCATExam