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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. The area of the plot which can be grazed by the horses is
- a)80 m2
- b)100 m2
- c)77 m2
- d)30 m2
Correct answer is option 'C'. Can you explain this answer?
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Three horses are tethered with 7 meter long ropes at the three corners...
**Given information:**
- Three horses are tethered at the three corners of a triangular field.
- The sides of the triangular field are 20 m, 34 m, and 42 m.
- Each horse is tethered with a 7 m long rope.
**To find:**
The area of the plot that can be grazed by the horses.
**Approach:**
1. Use the formula for the area of a triangle to find the area of the entire triangular field.
2. Find the lengths of the altitudes of the triangle.
3. Subtract the areas of the three smaller triangles formed by the ropes to find the area that can be grazed by the horses.
**Solution:**
1. Finding the area of the entire triangular field:
- Let the sides of the triangle be a = 20 m, b = 34 m, and c = 42 m.
- Use Heron's formula to find the area (A) of the triangle:
- Semi-perimeter (s) = (a + b + c) / 2
- s = (20 + 34 + 42) / 2 = 96 / 2 = 48
- Area (A) = √(s * (s - a) * (s - b) * (s - c))
- A = √(48 * (48 - 20) * (48 - 34) * (48 - 42))
- A = √(48 * 28 * 14 * 6) = √(56448) ≈ 237.75 m²
2. Finding the lengths of the altitudes of the triangle:
- The lengths of the altitudes can be found using the formula: h = (2 * A) / b
- Let h1, h2, and h3 be the lengths of the altitudes corresponding to sides a, b, and c, respectively.
- h1 = (2 * A) / a = (2 * 237.75) / 20 ≈ 23.78 m
- h2 = (2 * A) / b = (2 * 237.75) / 34 ≈ 13.97 m
- h3 = (2 * A) / c = (2 * 237.75) / 42 ≈ 11.32 m
3. Determining the areas of the smaller triangles formed by the ropes:
- Let s1, s2, and s3 be the sides of the smaller triangles formed by the ropes.
- s1 = h1 - 7 = 23.78 - 7 = 16.78 m
- s2 = h2 - 7 = 13.97 - 7 = 6.97 m
- s3 = h3 - 7 = 11.32 - 7 = 4.32 m
- Use Heron's formula to find the areas of the smaller triangles:
- Area1 = √(s1 * (s1 - h1) * (s1 - h2) * (s1 - h3))
- Area1 = √(16.78 * (16.78 - 23.78) * (16.78 - 13.97
- Three horses are tethered at the three corners of a triangular field.
- The sides of the triangular field are 20 m, 34 m, and 42 m.
- Each horse is tethered with a 7 m long rope.
**To find:**
The area of the plot that can be grazed by the horses.
**Approach:**
1. Use the formula for the area of a triangle to find the area of the entire triangular field.
2. Find the lengths of the altitudes of the triangle.
3. Subtract the areas of the three smaller triangles formed by the ropes to find the area that can be grazed by the horses.
**Solution:**
1. Finding the area of the entire triangular field:
- Let the sides of the triangle be a = 20 m, b = 34 m, and c = 42 m.
- Use Heron's formula to find the area (A) of the triangle:
- Semi-perimeter (s) = (a + b + c) / 2
- s = (20 + 34 + 42) / 2 = 96 / 2 = 48
- Area (A) = √(s * (s - a) * (s - b) * (s - c))
- A = √(48 * (48 - 20) * (48 - 34) * (48 - 42))
- A = √(48 * 28 * 14 * 6) = √(56448) ≈ 237.75 m²
2. Finding the lengths of the altitudes of the triangle:
- The lengths of the altitudes can be found using the formula: h = (2 * A) / b
- Let h1, h2, and h3 be the lengths of the altitudes corresponding to sides a, b, and c, respectively.
- h1 = (2 * A) / a = (2 * 237.75) / 20 ≈ 23.78 m
- h2 = (2 * A) / b = (2 * 237.75) / 34 ≈ 13.97 m
- h3 = (2 * A) / c = (2 * 237.75) / 42 ≈ 11.32 m
3. Determining the areas of the smaller triangles formed by the ropes:
- Let s1, s2, and s3 be the sides of the smaller triangles formed by the ropes.
- s1 = h1 - 7 = 23.78 - 7 = 16.78 m
- s2 = h2 - 7 = 13.97 - 7 = 6.97 m
- s3 = h3 - 7 = 11.32 - 7 = 4.32 m
- Use Heron's formula to find the areas of the smaller triangles:
- Area1 = √(s1 * (s1 - h1) * (s1 - h2) * (s1 - h3))
- Area1 = √(16.78 * (16.78 - 23.78) * (16.78 - 13.97
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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. The area of the plot which can be grazed by the horses isa)80 m2b)100 m2c)77 m2d)30 m2Correct answer is option 'C'. Can you explain this answer?
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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. The area of the plot which can be grazed by the horses isa)80 m2b)100 m2c)77 m2d)30 m2Correct answer is option 'C'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about 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. The area of the plot which can be grazed by the horses isa)80 m2b)100 m2c)77 m2d)30 m2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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. The area of the plot which can be grazed by the horses isa)80 m2b)100 m2c)77 m2d)30 m2Correct answer is option 'C'. Can you explain this answer?.
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. The area of the plot which can be grazed by the horses isa)80 m2b)100 m2c)77 m2d)30 m2Correct answer is option 'C'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about 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. The area of the plot which can be grazed by the horses isa)80 m2b)100 m2c)77 m2d)30 m2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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. The area of the plot which can be grazed by the horses isa)80 m2b)100 m2c)77 m2d)30 m2Correct answer is option 'C'. Can you explain this answer?.
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