Question

A horse is tethered to a peg with a 14 meter long rope at the corner of a 40 meter long and 24 meter wide rectangular grass field. what area of field will the hoese graze

Answer 1

radius = 14 meter
as shortest side (breadth) = 24 m, that implies that the are grazen by the horse  = quarter circle.
area = 1/4 x 22/7 x 14 x 14
= 11/14 x 14 x 14
= 11 x 14
= 154 metre square    ANSWER...


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Answer 2

Area of the grass field that the horse will graze is 154 sq. m.

• Length of the rope to which a horse is tied = 14 m

• Length and breadth of the grass field is 40 m and 24 m respectively.

• The horse is tied to one corner of the rectangular field.

• As the length of the rope is less than the length and breadth of the grass field, the area that the horse will graze will be equal to a sector with radius equal to the length of the rope and the angle made by the sector will be equal to 90°.

• Area of the sector is given by the formula ,

A = $\frac{\theta}{360} (\pi r^2)$

A = $\frac{90}{360} (\pi)( 14^2)$

A = $(\frac{1}{4})( \frac{22}{7})(14)(14)$

A = $(\frac{1}{4})( \frac{22}{7})(14)(14)$

A = 154 sq. m

• Area of the grass field that the horse will graze is 154 sq. m.