Puja has two ropes measuring 5 m and 6 m. She ties a goat at point A with the 5 m rope and ties another goat at point B with the 6 m rope. Find out the ratio of areas grazed at point A and point B. The goats can only move inside the field.

24:36

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25:37

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26:37

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25:36

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Solution

The correct option is D
25:36

The area grazed by both the goats will be circular in shape as they are moving at a constant distance from a fixed point.

Hence, the area grazed when a goat is tied at a point with a rope would be a circle with radius equal to the length of the rope.

Area of a circle = $π r^{2}$ .

Hence, the required ratio = $\frac{A r e a a t A}{A r e a a t B}$

= $(\frac{π r_{A}}{π r_{B}})^{2}$

= $(\frac{r_{A}}{r_{B}})^{2}$

= $(\frac{5}{6})^{2}$ = 25:36 .

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