Question

Sides of a triangular feild are 15m,16m,17m.With the three corners of a feild 3 cows are tied seperately with ropes of lenght 7 m.Find the area of the feild which cannot be grazed

Answer 1

Let the angles of the triangle be a,b & c ;

Area grazed by the cow
= area of a sector
= (∅/360)×πr²

1. Area grazed by 1st cow
= (a/360)×π×7²
= (a/360) × 22×7
= 77a/180

2. Area grazed by 2nd cow
= (b/360)×(22/7)×7²
= 77b/180

3. Area grazed by 3rd cow
= (c/360)×(22/7)×7²
= 77c/180

•Total area grazed by the cows

= (77a/180)+(77b/180)+(77c/180)
= (77/180) (a+b+c)
= (77/180)×(180)
-------(a+b+c=180° -> angle sum property of a triangle)
= 77 m²

Area that cannot be grazed
= area of triangle - 77m²
= √{24×(24-15)×(24-16)×(24-17)} - 77
= √(24×9×8×7) - 77
= √12096 - 77
= 32.98 m²
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