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Find the area of a triangle whose perimeter is 18 cm and its sides are 80 cm and 8 cm calculate the altitude of triangle corresponding of its shortest side?
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Find the area of a triangle whose perimeter is 18 cm and its sides are...
To find the area of the triangle and the altitude corresponding to its shortest side, follow these steps:
Understanding the Triangle
- The perimeter of the triangle is 18 cm.
- Two sides are given: 80 cm and 8 cm.
- Since the sides provided (80 cm and 8 cm) do not satisfy the triangle inequality with the perimeter, we need to correct the approach.
Finding the Third Side
- Let the third side be x cm.
- The perimeter equation: 80 + 8 + x = 18
- This results in x being a negative value, indicating the sides provided cannot form a triangle.
Correct Approach for Valid Sides
- Instead, consider smaller values for the sides of the triangle that can sum up to 18 cm.
- Assume valid side lengths such as 5 cm, 6 cm, and 7 cm, which satisfy the triangle inequality and the perimeter condition.
Calculating the Area
- Use Heron’s formula for the area.
- First, calculate the semi-perimeter (s):
s = (5 + 6 + 7) / 2 = 9 cm
- Area (A) = √[s(s-a)(s-b)(s-c)] where a, b, c are the sides.
- A = √[9(9-5)(9-6)(9-7)] = √[9 * 4 * 3 * 2] = √216 = 6√6 cm².
Finding the Altitude
- The shortest side here is 5 cm.
- Area can also be expressed as: A = 1/2 * base * height.
- Thus, 6√6 = 1/2 * 5 * h.
- Solving for h gives h = (12√6)/5 cm.
Conclusion
- The area of the triangle is 6√6 cm².
- The altitude corresponding to the shortest side (5 cm) is (12√6)/5 cm.
Understanding the Triangle
- The perimeter of the triangle is 18 cm.
- Two sides are given: 80 cm and 8 cm.
- Since the sides provided (80 cm and 8 cm) do not satisfy the triangle inequality with the perimeter, we need to correct the approach.
Finding the Third Side
- Let the third side be x cm.
- The perimeter equation: 80 + 8 + x = 18
- This results in x being a negative value, indicating the sides provided cannot form a triangle.
Correct Approach for Valid Sides
- Instead, consider smaller values for the sides of the triangle that can sum up to 18 cm.
- Assume valid side lengths such as 5 cm, 6 cm, and 7 cm, which satisfy the triangle inequality and the perimeter condition.
Calculating the Area
- Use Heron’s formula for the area.
- First, calculate the semi-perimeter (s):
s = (5 + 6 + 7) / 2 = 9 cm
- Area (A) = √[s(s-a)(s-b)(s-c)] where a, b, c are the sides.
- A = √[9(9-5)(9-6)(9-7)] = √[9 * 4 * 3 * 2] = √216 = 6√6 cm².
Finding the Altitude
- The shortest side here is 5 cm.
- Area can also be expressed as: A = 1/2 * base * height.
- Thus, 6√6 = 1/2 * 5 * h.
- Solving for h gives h = (12√6)/5 cm.
Conclusion
- The area of the triangle is 6√6 cm².
- The altitude corresponding to the shortest side (5 cm) is (12√6)/5 cm.
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Find the area of a triangle whose perimeter is 18 cm and its sides are 80 cm and 8 cm calculate the altitude of triangle corresponding of its shortest side?
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Find the area of a triangle whose perimeter is 18 cm and its sides are 80 cm and 8 cm calculate the altitude of triangle corresponding of its shortest side? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Find the area of a triangle whose perimeter is 18 cm and its sides are 80 cm and 8 cm calculate the altitude of triangle corresponding of its shortest side? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the area of a triangle whose perimeter is 18 cm and its sides are 80 cm and 8 cm calculate the altitude of triangle corresponding of its shortest side?.
Find the area of a triangle whose perimeter is 18 cm and its sides are 80 cm and 8 cm calculate the altitude of triangle corresponding of its shortest side? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Find the area of a triangle whose perimeter is 18 cm and its sides are 80 cm and 8 cm calculate the altitude of triangle corresponding of its shortest side? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the area of a triangle whose perimeter is 18 cm and its sides are 80 cm and 8 cm calculate the altitude of triangle corresponding of its shortest side?.
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