HCU MCA 2013 Paper

Question : 3 of 75

Marks: +1, -0

Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then, the ratio of the shorter side to the longer side is

$1/2$
$2/3$
$1/4$
$3/4$

Validate

Solution:

(d) Let the shorter and longer sides of a rectangle be x and y.
According to the given condition,

\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;√{\x^2+\y^2}=\x+\y/2

⇒

\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\x^2+\y^2=x^2+\y^2/2+\xy

⇒

\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{{3\y^2}/4=\xy

∴

\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\x/\y=3/4

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