The smallest possible circle, touching two opposite sides of a rectangle, is cut out from a rectangle of area 60 sq units. If the area of the circle is 1.5 times the uncut area left in the rectangle, find the diameter of the circle.
A (6/√π) units
B. (9/√π) units
C. (12/√π) units
D. (15/√π) units
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Answer:
B
Step-by-step explanation:
such shortest possible circle will be one touching only the breadth of rectangle
let area of circle be x and given that
area of circle= 1.5 times of uncut area
uncut area= x/1.5= 2x/3
uncut area = ar of rectangle- ar of circle
2x/3 =60-x
2x/3+ x =60
5x/3 =60
x=60×3/5 =36
pi r^2 = 36
r= 6/root pi
diameter= 2 x r= 12/ root pi
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