Question

A rectangle is drawn so that none of its sides has a length greater than 'x'. all lengths lesser than 'x' are equally likely. The chance that the rectangle has its diagonal greater than 'x' is (in %)?

• A. 29.3%
• B. 21.5%
• C. 66.66%
• D. 33.33%

Answer 1

The correct option is B

21.5%

Draw a square of side x and an arc of radius x.

All rectangles with diagonal less than or equal to x will lie within or on the quadrant of the circle. The unshaded region is the favorable area.
Hence, required probability = $\frac{x^2(1-\frac{\pi }{4})}{x^2}\times 100$ = 0.215 = 21.5% chance