Question

A horse is tied to a peg at one corner of a square field of length 25 m with a rope of length 7 m. If the length of the rope is increased to 10.5 m, find the percentage increase in the area of land that the horse can graze.

Answer 1

Step-by-step explanation:

Side of square=15m

Length of rope=5m=radius

The area available for horse to graze is nothing but "Area of Quadrant of a circle'

∴ Area of Quadrant = π×r^2/4 = 3.14×5×5/4

=19.625m^2

If the length of rope is increased to 10m then the new radius ,=10m

∴ Area of new quadrant = 3.14×10×10/4

=78.5m^2

∴ Increase in grazing area =78.5− 19.625= 58.875m^2

Answer 2

Answer:

percent increase in the area = 125%

Step-by-step explanation:

since the horse is tied at a corner of a square field, it can graze in a area of quarter circle with length of the rope as radius.

$earlier \: the \: length \: of \: rope \: was \: 7m. \\ hence \: the \: area \: of \: land \: that \: horse \: can \: graze \: = \frac{\pi}{4} \times {7}^{2} \\ = 38.5 \: {m}^{2} \\ \: if \: the \: length \: of \: rope \: is \: increased \: to \: 10.5 \: m \\ then \: the \: area \: of \: land \: that \: horse \: can \: graze \: = \frac{\pi}{4} \times {10.5}^{2} \\ = 86.625 {m}^{2} \\ percentage \: increase \: in \: the \: area \: of \: land \: is \\ = \frac{(86.625 - 38.5)}{38.5} \times 100 \\ = 125$