Question

Three horses are tethered at 3 corners of a triangular plot having sides 20 m, 30 m and 40 m with ropes of 7 m length each. Find the area of this plot which can be grazed by the horse.

Answer 1

area of the field grazed by the three horses is 77m^2... hoping that it helps you...

Answer 2

The area of plot which can be gazed by horse is $77 m^{2}$

Solution:

Let the three horses tied at point P, Q and R of the triangle.

The sides of triangle are 20m , 30m and 40m and the length of the rope is 7m

$\text { Let angle } P=\theta_{1} \text { angle } Q=\theta_{2} \text { and angle } R=\theta_{3}$

Area grazed by three animals = sum of the areas of 3 sectors with central angle θ1 , θ2 and θ3 and radius =7m

$=\frac{\pi r^{2} \theta 1}{360}+\frac{\pi r^{2} \theta 2}{360}+\frac{\pi r^{2} \theta 3}{360}=\frac{\pi r^{2}}{360}(\theta 1+\theta 2+\theta 3)$

By angle sum property of triangle, sum of all three angles in triangle is 180

$=\frac{\pi r^{2}}{360} \times 180=\frac{22 \times 7 \times 7}{7 \times 360} \times 180=77 m^{2}$

Thus the area gazed by horses is $77 m^{2}$

Learn more about area of triangle

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