geometry

Hello.

First of all, the following solution will give us the least length of the rope that allows the horse to graze over an area of 1100m^2. Second, I am going to assume that the rope will be tied to a stick in the center of a field, that is to say, the area in which the horse will graze will be a circle, whose radius is the length of the rope.

We want that the area of the circle mentioned will be greater than 1100m^2, this implies that we want to find r such that $$\pi\cdot r^2>1100 \ m^2\ \ \ \ \Rightarrow\ \ \ r>18.7\ m \ .$$ Hence, the length of the rope must be greater than 18.7 m.

According to the given options (and my assumption about the least length), the correct answer is the option A.

I really hope it helps.

vaibhav101 wrote:Find the length of the rope by which a horse must be tethered to in order that he may be allowed to graze over 1100 m^2.

A 18.7 m
B 21.5 m
C 20.25 m
D 24.7 m
E 22.5 m

The area a horse can graze when it is tethered by a rope is the area of a circle, with the rope being the length of the radius of the circle. If we let the length of the rope be r, we have:

πr^2 = 1100

r^2 = 1100/π

r = √(1100/π)

r ≈ 18.7

Answer: A