A horse is tied to a post by a rope. If the horse moves along a circular path, always keeping the rope tight, and describes 88 m when it traces 72^ at - Geometry MCQ Competitive Exams 2026 | ExamTest.live

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A horse is tied to a post by a rope. If the horse moves along a circular path, always keeping the rope tight, and describes 88 m when it traces 7 2^{\circ} at the centre, then the length of the rope is

Solution & Step-by-step Explanation

The path traced by the horse is an arc of a circle whose radius (r) is equal to the length of the tight rope. The formula for the length of an arc is: Arc Length (l) = \frac{θ}{36 0 ^{\circ}} \times 2 π r Given l = 88 m and θ = 7 2^{\circ} : 88 = \frac{72}{360} \times 2 \times \frac{22}{7} \times r Since \frac{72}{360} = \frac{1}{5} : 88 = \frac{1}{5} \times \frac{44}{7} \times r 88 = \frac{44}{35} \times r r = 88 \times \frac{35}{44} = 2 \times 35 = 70 m Therefore, the length of the rope is 70 m .

Try it yourself before checking the explanation above.

A horse is tied to a post by a rope. If the horse moves along a circular path, always keeping the rope tight, and describes 88 m when it traces 7 2^{\circ} at the centre, then the length of the rope is

35 m

70 m

17.5 m

22 m

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