Question

Instead of walking along two adjacent sides of a rectangular field,a boy book a short - cut along the diagonal of the field and saved a distance equal to 1/2 the longer side. The ratio of the shorter side of the rectangle to the longer side was:.

• A. $\frac{1}{2}$
• B. $\frac{2}{3}$
• C. $\frac{1}{4}$
• D. $\frac{3}{4}$
• E. $\frac{2}{5}$

Answer 1

Answer: (D)

$\frac{3}{4}$

Let a and b be the sides of the rectangle.

$⟹(a+b)-\sqrt{a^2+b^2}=\frac{a}{2}⟹\frac{a}{2}+b=\sqrt{a^2+b^2}⟹\frac{a^2}{4}+b^2+ab=a^2+b^2⟹ab=\frac{{3a}^2}{4}⟹\frac{b}{a}=\frac{3}{4}$

$\therefore$ Ratio of shorter side to longer side = $\frac{3}{4}$