Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
A kite-shaped quadrilateral of the largest possible area is cut from a circular sheet of paper. If the lengths of the sides of the kite are in the ratio 3 : 3 : 4 : 4, what percentage of the circular sheet is wasted?
(a)34\%
(b)39\%
(c)42\%
(d)47\%
Answer
Answer (as printed): B
Explanation
Clearly, the longer diagonal of the kite is the diameter of the circle. Also, $\angle A B C=90^{\circ}$ (angle in a semi-circle) Let $A B=A D=3 x$ and $B C=C D=4 x$. Then, $A C=\sqrt{A B^{2}+B C^{2}}=5 x$. Area of the kite $=2 \times$ area $(\triangle A B C)$ $=2 \times \frac{1}{2} \times B C \times A B=3 x \times 4 x=12 x^{2}$. Area of the circle $=\pi r^{2}=\left(\frac{22}{7} \times \frac{5 x}{2} \times \frac{5 x}{2}\right)=\frac{275}{14} x^{2}$. Area wasted $=\left(\frac{275}{14} x^{2}-12 x^{2}\right)=\frac{107}{14} x^{2}$. Required percentage $=\left(\frac{107}{14} \times \frac{14}{275} \times 100\right) \%=39 \%$.
Explanation as extracted from the printed page; notation may be imperfect.