NIMCET 2012 Question Paper with solutions

Question : 75 of 120

Marks: +1, -0

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

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

Validate

Solution:

Let longer side = x = DC
and shorter side = y = AD

Now, by condition,
AC = y +

x/2

Now, In Δ ACD,

AC^2

AD^2+CD^2

(by Pythagoras theorem)
⇒

(y+x/2)^2

y^2+x^2

⇒

y^2+x^2/4

+ xy =

z^2+y^2

⇒

x^2/4

+ xy -

x^2

= 0
⇒ x

\{x/4+y-x\}

= 0
⇒ x

(y-{3x}/4)

= 0
⇒

y/x = 3/4

Since x ≠ 0

Go to Question:

Prev Question

Next Question