Published by:
CGP EDU Academic Team
Published on: August 14, 2026
A running track of 440 ft. is to be laid out enclosing a football field, the shape of which is a rectangle with a semi-circle at each end. If the area of the rectangular portion is to be maximum then the lengths of its sides are -
Text Solution
Verified by ExpertsThe correct answer is:
A
Perimeter = 440 ft.
2x + π r + π r = 440
or 2x + 2 π r = 440 … (1)
A = Area of rectangular portion = x . 2r
A = x 
= 
(440x – 2x 2 )
= 
(440 – 4x) ∴ x = 110
= –ive
∴ A is max. when x = 110
∴ 2r = 
= 
= 70.
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