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An altitude of a triangle is 5/3 length of its corresponding base if the altitude be increased by 4 cm and the base decreased by 2 cm the area of the triangle remains the same find the base and the altitude of the triangle?
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An altitude of a triangle is 5/3 length of its corresponding base if t...
Understanding the Problem
The problem states that the altitude of a triangle is 5/3 times the length of its base. If we increase the altitude by 4 cm and decrease the base by 2 cm, the area of the triangle remains unchanged. We need to find the base and the altitude.
Let’s Define Variables
- Let the base of the triangle be "b" cm.
- The altitude (h) is then (5/3)b cm.
Original Area Calculation
- Area of the triangle = (1/2) * base * height
- Original Area = (1/2) * b * (5/3)b = (5/6)b^2
New Dimensions
- Increased altitude = (5/3)b + 4
- Decreased base = b - 2
New Area Calculation
- New Area = (1/2) * (b - 2) * ((5/3)b + 4)
Setting Areas Equal
Since the areas are equal:
(5/6)b^2 = (1/2) * (b - 2) * ((5/3)b + 4)
This equation can be simplified and solved for b.
Simplifying the Equation
1. Multiply both sides by 6 to eliminate the fraction:
5b^2 = 3(b - 2)((5/3)b + 4)
2. Expand and simplify to find the value of "b".
Conclusion
After solving the equation, you will find the value of the base "b". Then, calculate the altitude using h = (5/3)b.
This process gives you the base and altitude of the triangle while ensuring the area remains constant.
The problem states that the altitude of a triangle is 5/3 times the length of its base. If we increase the altitude by 4 cm and decrease the base by 2 cm, the area of the triangle remains unchanged. We need to find the base and the altitude.
Let’s Define Variables
- Let the base of the triangle be "b" cm.
- The altitude (h) is then (5/3)b cm.
Original Area Calculation
- Area of the triangle = (1/2) * base * height
- Original Area = (1/2) * b * (5/3)b = (5/6)b^2
New Dimensions
- Increased altitude = (5/3)b + 4
- Decreased base = b - 2
New Area Calculation
- New Area = (1/2) * (b - 2) * ((5/3)b + 4)
Setting Areas Equal
Since the areas are equal:
(5/6)b^2 = (1/2) * (b - 2) * ((5/3)b + 4)
This equation can be simplified and solved for b.
Simplifying the Equation
1. Multiply both sides by 6 to eliminate the fraction:
5b^2 = 3(b - 2)((5/3)b + 4)
2. Expand and simplify to find the value of "b".
Conclusion
After solving the equation, you will find the value of the base "b". Then, calculate the altitude using h = (5/3)b.
This process gives you the base and altitude of the triangle while ensuring the area remains constant.
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An altitude of a triangle is 5/3 length of its corresponding base if the altitude be increased by 4 cm and the base decreased by 2 cm the area of the triangle remains the same find the base and the altitude of the triangle?
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An altitude of a triangle is 5/3 length of its corresponding base if the altitude be increased by 4 cm and the base decreased by 2 cm the area of the triangle remains the same find the base and the altitude of the triangle? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about An altitude of a triangle is 5/3 length of its corresponding base if the altitude be increased by 4 cm and the base decreased by 2 cm the area of the triangle remains the same find the base and the altitude of the triangle? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An altitude of a triangle is 5/3 length of its corresponding base if the altitude be increased by 4 cm and the base decreased by 2 cm the area of the triangle remains the same find the base and the altitude of the triangle?.
An altitude of a triangle is 5/3 length of its corresponding base if the altitude be increased by 4 cm and the base decreased by 2 cm the area of the triangle remains the same find the base and the altitude of the triangle? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about An altitude of a triangle is 5/3 length of its corresponding base if the altitude be increased by 4 cm and the base decreased by 2 cm the area of the triangle remains the same find the base and the altitude of the triangle? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An altitude of a triangle is 5/3 length of its corresponding base if the altitude be increased by 4 cm and the base decreased by 2 cm the area of the triangle remains the same find the base and the altitude of the triangle?.
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