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The sides of two squares are in the ratio 3:4. Find the ratio of their areas.?
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The sides of two squares are in the ratio 3:4. Find the ratio of their...
To find the ratio of the areas of two squares when the sides are in the ratio of 3:4, follow these steps:
Understanding the Sides of the Squares
- Let the side of the first square be 3x.
- Let the side of the second square be 4x.
Calculating the Areas of the Squares
- The area of a square is calculated using the formula:
Area = side × side
- For the first square:
Area₁ = (3x) × (3x) = 9x²
- For the second square:
Area₂ = (4x) × (4x) = 16x²
Finding the Ratio of the Areas
- To find the ratio of the areas of the two squares, we calculate:
Ratio of Areas = Area₁ : Area₂ = 9x² : 16x²
- Simplifying this gives:
Ratio of Areas = 9 : 16
Conclusion
- The ratio of the areas of the two squares is 9:16.
- This means that for every 9 square units of area the first square has, the second square has 16 square units of area.
This clear relationship between side lengths and areas illustrates how the area increases with the square of the side length, emphasizing the importance of understanding geometry in mathematical problems.
Understanding the Sides of the Squares
- Let the side of the first square be 3x.
- Let the side of the second square be 4x.
Calculating the Areas of the Squares
- The area of a square is calculated using the formula:
Area = side × side
- For the first square:
Area₁ = (3x) × (3x) = 9x²
- For the second square:
Area₂ = (4x) × (4x) = 16x²
Finding the Ratio of the Areas
- To find the ratio of the areas of the two squares, we calculate:
Ratio of Areas = Area₁ : Area₂ = 9x² : 16x²
- Simplifying this gives:
Ratio of Areas = 9 : 16
Conclusion
- The ratio of the areas of the two squares is 9:16.
- This means that for every 9 square units of area the first square has, the second square has 16 square units of area.
This clear relationship between side lengths and areas illustrates how the area increases with the square of the side length, emphasizing the importance of understanding geometry in mathematical problems.
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The sides of two squares are in the ratio 3:4. Find the ratio of their areas.?
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The sides of two squares are in the ratio 3:4. Find the ratio of their areas.? for Class 6 2024 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about The sides of two squares are in the ratio 3:4. Find the ratio of their areas.? covers all topics & solutions for Class 6 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sides of two squares are in the ratio 3:4. Find the ratio of their areas.?.
The sides of two squares are in the ratio 3:4. Find the ratio of their areas.? for Class 6 2024 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about The sides of two squares are in the ratio 3:4. Find the ratio of their areas.? covers all topics & solutions for Class 6 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sides of two squares are in the ratio 3:4. Find the ratio of their areas.?.
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