CAT 2015 Quantitative Ability

Question : 3 of 34

Marks: +1, -0

The smallest possible circle touching two opposite sides of a rectangle is cut-out from a rectangle of area 60 sq. units. If the area of this circle is

3/2

times the area left out in the rectangle, find the length of the smaller side of the rectangle.

$6/√π$ units
$9/√π$ units
$12/√π$ units
$15/√π$ units

Validate

Solution:

Let ‘a’ be the length of smaller side

∴\;\;\text"Radius" = a/2

⇒ \;\;π(\;\;{a}/{2})^{2}=\;\;{3}/{2}[60-π(\;\;{a}/{2})^{2}]

⇒ \;\;5π(\;\;{a}/{2})^{2}=180

⇒\;\;{πa^{2}}/{4}=36

a=√{\;\;{36×4}/{π}}=\;\;{12}/{√{π}}\;\text"units"\;

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