Sides of a right triangular field are 25 m, 24 m and 7m. At the three corners of the field, a cow, a buffalo and a horse are tied separately with ropes of 3.5 m each to graze in the field. Find the area of the field that cannot be grazed by these animals.

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  1. Class 10
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Transcript

Question 33 Sides of a right triangular field are 25 m, 24 m and 7m. At the three corners of the field, a cow, a buffalo and a horse are tied separately with ropes of 3.5 m each to graze in the field. Find the area of the field that cannot be grazed by these animals. Here, the animals graze area of sectors Area of the field that cannot be grazed = Area of Δ ABC – Area of sectors grazed by all 3 animals Area of Δ ABC Δ ABC is a right angled triangle with Base = 7 m Height = 24 m Area of Δ ABC = 1/2 × Base × Height = 1/2 × 24 × 7 = 12 × 7 = 84 m2 Area of Sector grazed by all three animals We know that Area of sector = 𝜃/(360°) × πr2 And radius = 3.5 m Area of Sector at point A = (∠𝐴)/(360°) × πr2 Area of Sector at point B = (∠𝐵)/(360°) × πr2 Area of Sector at point C = (∠𝐶)/(360°) × πr2 Therefore, Area of sector grazed by all 3 animals = (∠𝐴)/(360°) × πr2 + (∠𝐵)/(360°) × πr2 + (∠𝐶)/(360°) × πr2 = 1/(360°) × πr2 (∠ A + ∠ B + ∠ C) Since sum of angles of a triangle = 180° = 1/(360°) × πr2 × 180° = 1/2 × πr2 Putting r = 3.5 m = 1/2 × 22/7 × (3.5)2 = 11/7 × 3.5 × 3.5 = 11 × 0.5 × 3.5 = 19.25 m2 Hence, Area of the field that cannot be grazed = Area of Δ ABC – Area of sectors grazed by all 3 animals = 84 – 19.25 = 64.75 m2

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.