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If each side of triangle is increased by 4 times . find ratio of new area to old area?
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If each side of triangle is increased by 4 times . find ratio of new a...
Understanding Triangle Area
The area of a triangle can be calculated using the formula:
Area = 1/2 * base * height.
When each side of a triangle is scaled by a factor, the area changes according to the square of that factor.
Scaling Factor
In this case, each side of the triangle is increased by 4 times.
- Original side length = s
- New side length = 4s
Effect on Area
Since the area of a triangle scales with the square of the side length factor:
- The scaling factor for area = (4)^2 = 16.
New Area Calculation
Thus, if the original area is A, the new area (A_new) can be calculated as follows:
- A_new = 16 * A.
Ratio of New Area to Old Area
The ratio of the new area to the old area is:
- Ratio = New Area / Old Area = A_new / A = 16A / A = 16.
Conclusion
Therefore, when each side of a triangle is increased by 4 times, the ratio of the new area to the old area is:
- 16:1.
This means the new area is 16 times greater than the original area, showcasing how significantly scaling affects geometric figures.
The area of a triangle can be calculated using the formula:
Area = 1/2 * base * height.
When each side of a triangle is scaled by a factor, the area changes according to the square of that factor.
Scaling Factor
In this case, each side of the triangle is increased by 4 times.
- Original side length = s
- New side length = 4s
Effect on Area
Since the area of a triangle scales with the square of the side length factor:
- The scaling factor for area = (4)^2 = 16.
New Area Calculation
Thus, if the original area is A, the new area (A_new) can be calculated as follows:
- A_new = 16 * A.
Ratio of New Area to Old Area
The ratio of the new area to the old area is:
- Ratio = New Area / Old Area = A_new / A = 16A / A = 16.
Conclusion
Therefore, when each side of a triangle is increased by 4 times, the ratio of the new area to the old area is:
- 16:1.
This means the new area is 16 times greater than the original area, showcasing how significantly scaling affects geometric figures.
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If each side of triangle is increased by 4 times . find ratio of new area to old area?
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If each side of triangle is increased by 4 times . find ratio of new area to old area? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If each side of triangle is increased by 4 times . find ratio of new area to old area? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If each side of triangle is increased by 4 times . find ratio of new area to old area?.
If each side of triangle is increased by 4 times . find ratio of new area to old area? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If each side of triangle is increased by 4 times . find ratio of new area to old area? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If each side of triangle is increased by 4 times . find ratio of new area to old area?.
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