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 %)?
Answer: Option B
:
B
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 = x2(1−π4)x2×100= 0.215 = 21.5% chance
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:
B
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 = x2(1−π4)x2×100= 0.215 = 21.5% chance
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