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The floor of a rectangular hall has been decorated by a rectangular carpet having its two adjacent sides as 7a^2+14ab+6b^2 and 3a^2 -9ab +4b^2. FIND ITS AREA? Also explain the factorization in a simpler way.?
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The floor of a rectangular hall has been decorated by a rectangular ca...
Calculating the Area of the Carpet
Firstly, we need to find the dimensions of the rectangular carpet by factoring the expressions given for its adjacent sides.
Factorizing the Expressions
Given:
1. Length of the carpet = 7a^2 + 14ab + 6b^2
2. Width of the carpet = 3a^2 - 9ab + 4b^2
By factoring each expression, we get:
1. Length = (2a + b)(3a + 2b)
2. Width = (a - 2b)(3a - 2b)
Calculating the Area
To find the area of the carpet, we multiply the length by the width:
Area = Length x Width
Area = (2a + b)(3a + 2b)(a - 2b)(3a - 2b)
Simplify the Expression
Now, we multiply the factors to simplify the expression and find the final area of the carpet.
After simplifying the expression, we get the area of the rectangular carpet in terms of a and b.
Conclusion
In conclusion, the area of the rectangular carpet with the given dimensions can be calculated by factoring the expressions for its adjacent sides, then multiplying the length and width to find the total area. This method ensures an accurate calculation of the carpet's area based on the provided expressions for its dimensions.
Firstly, we need to find the dimensions of the rectangular carpet by factoring the expressions given for its adjacent sides.
Factorizing the Expressions
Given:
1. Length of the carpet = 7a^2 + 14ab + 6b^2
2. Width of the carpet = 3a^2 - 9ab + 4b^2
By factoring each expression, we get:
1. Length = (2a + b)(3a + 2b)
2. Width = (a - 2b)(3a - 2b)
Calculating the Area
To find the area of the carpet, we multiply the length by the width:
Area = Length x Width
Area = (2a + b)(3a + 2b)(a - 2b)(3a - 2b)
Simplify the Expression
Now, we multiply the factors to simplify the expression and find the final area of the carpet.
After simplifying the expression, we get the area of the rectangular carpet in terms of a and b.
Conclusion
In conclusion, the area of the rectangular carpet with the given dimensions can be calculated by factoring the expressions for its adjacent sides, then multiplying the length and width to find the total area. This method ensures an accurate calculation of the carpet's area based on the provided expressions for its dimensions.
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The floor of a rectangular hall has been decorated by a rectangular carpet having its two adjacent sides as 7a^2+14ab+6b^2 and 3a^2 -9ab +4b^2. FIND ITS AREA? Also explain the factorization in a simpler way.?
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The floor of a rectangular hall has been decorated by a rectangular carpet having its two adjacent sides as 7a^2+14ab+6b^2 and 3a^2 -9ab +4b^2. FIND ITS AREA? Also explain the factorization in a simpler way.? for Class 5 2024 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 exam syllabus. Information about The floor of a rectangular hall has been decorated by a rectangular carpet having its two adjacent sides as 7a^2+14ab+6b^2 and 3a^2 -9ab +4b^2. FIND ITS AREA? Also explain the factorization in a simpler way.? covers all topics & solutions for Class 5 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The floor of a rectangular hall has been decorated by a rectangular carpet having its two adjacent sides as 7a^2+14ab+6b^2 and 3a^2 -9ab +4b^2. FIND ITS AREA? Also explain the factorization in a simpler way.?.
The floor of a rectangular hall has been decorated by a rectangular carpet having its two adjacent sides as 7a^2+14ab+6b^2 and 3a^2 -9ab +4b^2. FIND ITS AREA? Also explain the factorization in a simpler way.? for Class 5 2024 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 exam syllabus. Information about The floor of a rectangular hall has been decorated by a rectangular carpet having its two adjacent sides as 7a^2+14ab+6b^2 and 3a^2 -9ab +4b^2. FIND ITS AREA? Also explain the factorization in a simpler way.? covers all topics & solutions for Class 5 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The floor of a rectangular hall has been decorated by a rectangular carpet having its two adjacent sides as 7a^2+14ab+6b^2 and 3a^2 -9ab +4b^2. FIND ITS AREA? Also explain the factorization in a simpler way.?.
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