Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
What is the length of the line SQ which is the diagonal of a square as well as the diameter of a circle? I. All the four vertices of the square lie on the circumference of the circle. II. The numerical value of the area of the circle is twice the length of SQ.
Answer
SELF-PRACTICE — the source book printed no answer.
Nothing is invented here, so this question has no answer on record.
Explanation
Let the length of SQ be $x$. Then, radius of the circle $=\frac{x}{2}$. I. The fact given in the question can be inferred form the information given in I. II. $\pi\left(\frac{x}{2}\right)^{2}=2 x \Rightarrow \frac{\pi x^{2}}{4}=2 x$ $$\Rightarrow \pi x^{2}=8 x \Rightarrow \pi x=8 \Rightarrow x=\frac{8 \times 7}{22}=\frac{28}{11} .$$ Thus, II alone gives the answer.
Explanation as extracted from the printed page; notation may be imperfect.