Question

a horse is tied with a rope of length 7 m at the corner of triangular field of side 3m each . if horse can't enter the triangle find the area that can be grazed by horse
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Answer 1

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Three horses are tethered with 7-meter-long ropes at the three corners of a triangular field having sides 20 m, 34 m and 42 m. Find the area of the plot which can be grazed by the horses and the area of the plot which remains ungrazed.

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Solution

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Correct option is

A

77m

2

; 259m

2

Given,

Sides of triangular field is 20m,34mand42m

Semi-perimeter =

2

20m+34m+42m

=

2

96

=48m

Area of field=

48(48−20)(48−34)(48−42)

=

48×28×14×6

=

112896

=336m

2

We know that sum of angles of triangles =180

Thus, Area gazed

=Area of sector APQ+Area of sector BRS+Area of sector CTU

=Area of semicircle with radius 7m

=

2

π

×(7m)

2

=

14

22

×(49m)

2

=77m

2

Area of field-Area of gazed

=(336−77)m

2

=259m

2

Area of ungazed is 259m