Question

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

• A. $\frac{1}{2}$
• B. $\frac{2}{3}$
• C. $\frac{1}{4}$
• D. $\frac{3}{4}$

Answer 1

Answer: (D)

$\frac{3}{4}$

Let the longer side be of length $l$.
Let the shorter side be of length $b$
Then according to the statement, distance saved is:
$(l+b)-\sqrt{l^2+b^2}=\frac{l}{2}$
$l+b-\frac{l}{2}=\sqrt{l^2+b^2}$

$l+2b=2\sqrt{l^2+b^2}$

$l^2+4b^2+4lb=4l^2+4b^2$

$3l^2-4lb=0$

$l(3l-4b)=0$

$\therefore \frac{b}{l}=\frac{3}{4}$