# Three horses are tied at 3 corners of a triangular plot having sides 30m, 40m and 50m with ropes of 7 m length each. Find the area where the horses can graze?

Lets assume that the three horses are tied at point A, B and C of the triangle ABC.

The sides of triangle are 30m , 40m and 50m and the length of the rope is 7m

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

$=\pi r^2 \frac{\theta_1}{360}+\pi r^2 \frac{\theta_2}{360}+\pi r^2 \frac{\theta_3}{360}\\ =\pi r^2 \frac{[\theta_1+\theta_2+\theta_3]}{360}\\ =\pi r^2 \frac{180}{360}\\ =\frac{22}{7} \times 7^2 \times \frac{1}{2}\\ = 77 \ m^2$

Thus the area gazed by horses is 77 m2.

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