Question

A goat is tied to a corner of a rectangular plot of dimension 14×17 m with a rope 21m long .It cannot graze inside the plot but can graze outside find the area it can graze

Answer 1

The area goat can graze is $346.5 m^2$.

Step-by-step explanation:  

Given:

Here as shown in the figure below, let us assume that ABCD be the rectangular plot.

And also let the horse is tied at the corner A of the field with a rope of length 21 m.

So, let AL =  AM = 21 m

Now, horse will be able to graze in the ALOM region of the rectangular plot.

Since each angle of a rectangle is a right angle, so ∠A = 90°.

Now, region ALOM forms a sector, with sector angle 90° and radius = 21 cm.

So, sector angle, θ = 90°and radius, r = 21 cm

Area of sector ALOM = $\frac{\theta}{360} \times \pi r^2$

                                    = $\frac{90}{360}\times \frac22}{7}\times (21)^2$

                                    = $\frac{1}{4}\times \frac22}{7}\times (21)^2$

                                     = $\frac{1}{4}\times \frac22}{7}\times (21 \times 21)$

                                     = $\frac{1}{2}\times 11\times 3 \times 21$

                                     = $\frac{693}{2}$

                                     = $346.5 m^2$

Therefore, the area goat can graze is $346.5 m^2$.