Question

A horse is tied to one corner of a rectangular field, $60$ m by $40$ m, by a rope $14$ m long. How much area can the horse graze?

• A. $150{\text{m}}^2$
• B. $154{\text{m}}^2$
• C. $160{\text{m}}^2$
• D. $165{\text{m}}^2$

Answer 1

Answer: (B)

$154{\text{m}}^2$

Make a rectangle with vertex say $A$ , $B$, $C$ and $D$.

Let us say horse is tied at corner $A$.

Angle $DAB$ is equal to $90°$.

Radius $=$ $14$ cm.

Area graze by horse $=\frac{\theta }{360}\times \pi r^2$.

$\Rightarrow \frac{90}{360}\times \pi \times 14\times 14=154{\text{m}}^2$.

So, option B is correct.