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The perimeter of a triangular field is 240 dm. If two of its sides are 78 dm and 50 dm, find the length of the perpendicular on the side of length 50 dm from the opposite vertex.?
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The perimeter of a triangular field is 240 dm. If two of its sides are...
Given Information:
- Perimeter of the triangular field = 240 dm
- Length of side A = 78 dm
- Length of side B = 50 dm
Finding the Length of Side C:
To find the length of the third side (C), we can use the formula for the perimeter of a triangle:
- Side C = Perimeter - (Side A + Side B)
Calculating:
- Side C = 240 dm - (78 dm + 50 dm)
- Side C = 240 dm - 128 dm
- Side C = 112 dm
Applying Heron's Formula:
To find the area of the triangle, we can use Heron’s formula, which requires the semi-perimeter (s):
- Semi-perimeter (s) = Perimeter / 2
- s = 240 dm / 2 = 120 dm
Now, we can find the area (A) using Heron’s formula:
- A = √[s * (s - A) * (s - B) * (s - C)]
- A = √[120 * (120 - 78) * (120 - 50) * (120 - 112)]
- A = √[120 * 42 * 70 * 8]
Calculating the area gives us:
- A = √(120 * 42 * 70 * 8)
Finding the Perpendicular Height:
To find the height (h) from the vertex opposite the side of length 50 dm, we can use the area formula:
- Area = 0.5 * base * height
- h = (2 * Area) / base
Here, the base is 50 dm:
- h = (2 * Area) / 50
By substituting the area value calculated previously, you can find the height. This will provide the length of the perpendicular from the opposite vertex to the side of length 50 dm.
- Perimeter of the triangular field = 240 dm
- Length of side A = 78 dm
- Length of side B = 50 dm
Finding the Length of Side C:
To find the length of the third side (C), we can use the formula for the perimeter of a triangle:
- Side C = Perimeter - (Side A + Side B)
Calculating:
- Side C = 240 dm - (78 dm + 50 dm)
- Side C = 240 dm - 128 dm
- Side C = 112 dm
Applying Heron's Formula:
To find the area of the triangle, we can use Heron’s formula, which requires the semi-perimeter (s):
- Semi-perimeter (s) = Perimeter / 2
- s = 240 dm / 2 = 120 dm
Now, we can find the area (A) using Heron’s formula:
- A = √[s * (s - A) * (s - B) * (s - C)]
- A = √[120 * (120 - 78) * (120 - 50) * (120 - 112)]
- A = √[120 * 42 * 70 * 8]
Calculating the area gives us:
- A = √(120 * 42 * 70 * 8)
Finding the Perpendicular Height:
To find the height (h) from the vertex opposite the side of length 50 dm, we can use the area formula:
- Area = 0.5 * base * height
- h = (2 * Area) / base
Here, the base is 50 dm:
- h = (2 * Area) / 50
By substituting the area value calculated previously, you can find the height. This will provide the length of the perpendicular from the opposite vertex to the side of length 50 dm.
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The perimeter of a triangular field is 240 dm. If two of its sides are 78 dm and 50 dm, find the length of the perpendicular on the side of length 50 dm from the opposite vertex.?
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The perimeter of a triangular field is 240 dm. If two of its sides are 78 dm and 50 dm, find the length of the perpendicular on the side of length 50 dm from the opposite vertex.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The perimeter of a triangular field is 240 dm. If two of its sides are 78 dm and 50 dm, find the length of the perpendicular on the side of length 50 dm from the opposite vertex.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The perimeter of a triangular field is 240 dm. If two of its sides are 78 dm and 50 dm, find the length of the perpendicular on the side of length 50 dm from the opposite vertex.?.
The perimeter of a triangular field is 240 dm. If two of its sides are 78 dm and 50 dm, find the length of the perpendicular on the side of length 50 dm from the opposite vertex.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The perimeter of a triangular field is 240 dm. If two of its sides are 78 dm and 50 dm, find the length of the perpendicular on the side of length 50 dm from the opposite vertex.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The perimeter of a triangular field is 240 dm. If two of its sides are 78 dm and 50 dm, find the length of the perpendicular on the side of length 50 dm from the opposite vertex.?.
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