The area of a rectangle is x² + 12xy + 27y² and its length is (x + 9y). Find the breadth of the rectangle.
Solution:
Area of a rectangle = Length × Breadth
∴ Breadth = Area / Length
Breadth = (x² + 12xy + 27y²) / (x + 9y)
= (x² + 9xy + 3xy + 27y²) / (x + 9y)
= [x(x + 9y) + 3y(x + 9y)] / (x + 9y)
= [(x + 3y) (x + 9y)] / (x + 9y)
= (x + 3y)
✦ Try This: The area of the rectangle is 10x² + 9xy + 2y² and its length is 5x + 2y. Find the breadth of the rectangle.
Area of a rectangle = Length × Breadth
∴ Breadth = Area / Length
Breadth = (10x² + 9xy + 2y²) / (5x + 2y)
=(10x² + 5xy +4xy+ 2y²)/(5x + 2y)
=(5x(2x + y) + 2y(2x + y))/(5x + 2y)
=(5x + 2y)(2x + y)/(5x + 2y)
= 2x + y
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9
NCERT Exemplar Class 8 Maths Chapter 7 Sample Problem 16
The area of a rectangle is x² + 12xy + 27y² and its length is (x + 9y). Find the breadth of the rectangle
Summary:
Given that the area of a rectangle is x² + 12xy + 27y² and its length is (x + 9y). The breadth of the rectangle is (x + 3y).
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