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The sides of a triangular plot are in the ratio of 6 : 7 : 8 and its perimeter is 420 m. Find its area.?
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The sides of a triangular plot are in the ratio of 6 : 7 : 8 and its p...
Given Data:
- The sides of the triangular plot are in the ratio of 6 : 7 : 8.
- The perimeter of the triangular plot is 420 m.
Finding the Lengths of Sides:
- Let the common ratio be x.
- Therefore, the lengths of the sides are 6x, 7x, and 8x.
- Sum of the sides = Perimeter of the triangle
- 6x + 7x + 8x = 420
- 21x = 420
- x = 20
- So, the lengths of the sides are 120 m, 140 m, and 160 m.
Calculating the Area of the Triangle:
- Let a, b, and c be the sides of the triangle.
- Using Heron's formula, the area of the triangle is √[s(s-a)(s-b)(s-c)], where s is the semi-perimeter.
- s = (a + b + c) / 2 = (120 + 140 + 160) / 2 = 210
- Area = √[210(210-120)(210-140)(210-160)]
- Area = √[210*90*70*50] = √(661500000) = 25750 sq. m
Conclusion:
- The area of the triangular plot is 25750 sq. m.
- The sides of the triangular plot are in the ratio of 6 : 7 : 8.
- The perimeter of the triangular plot is 420 m.
Finding the Lengths of Sides:
- Let the common ratio be x.
- Therefore, the lengths of the sides are 6x, 7x, and 8x.
- Sum of the sides = Perimeter of the triangle
- 6x + 7x + 8x = 420
- 21x = 420
- x = 20
- So, the lengths of the sides are 120 m, 140 m, and 160 m.
Calculating the Area of the Triangle:
- Let a, b, and c be the sides of the triangle.
- Using Heron's formula, the area of the triangle is √[s(s-a)(s-b)(s-c)], where s is the semi-perimeter.
- s = (a + b + c) / 2 = (120 + 140 + 160) / 2 = 210
- Area = √[210(210-120)(210-140)(210-160)]
- Area = √[210*90*70*50] = √(661500000) = 25750 sq. m
Conclusion:
- The area of the triangular plot is 25750 sq. m.
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The sides of a triangular plot are in the ratio of 6 : 7 : 8 and its perimeter is 420 m. Find its area.?
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The sides of a triangular plot are in the ratio of 6 : 7 : 8 and its perimeter is 420 m. Find its area.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The sides of a triangular plot are in the ratio of 6 : 7 : 8 and its perimeter is 420 m. Find its area.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sides of a triangular plot are in the ratio of 6 : 7 : 8 and its perimeter is 420 m. Find its area.?.
The sides of a triangular plot are in the ratio of 6 : 7 : 8 and its perimeter is 420 m. Find its area.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The sides of a triangular plot are in the ratio of 6 : 7 : 8 and its perimeter is 420 m. Find its area.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sides of a triangular plot are in the ratio of 6 : 7 : 8 and its perimeter is 420 m. Find its area.?.
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