# 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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