The area of a rectangle is x² + 7x + 12. If its breadth is (x + 3), then find its length.

Solution:

Area of the rectangle = length × breadth

Given that the area of the rectangle is x² + 7x + 12 and breadth (x + 3)

∴ Area of the rectangle = x² + 7x + 12 = length × (x + 3)

Length = (x² + 7x + 12) / (x + 3)

= (x² + 4x + 3x + 12) / (x + 3)

= [x(x + 4) + 3(x + 4)] / (x + 3)

= [(x + 3) (x + 4)] / (x + 3)

= (x + 4)

✦ Try This: The area of the rectangle is 2x² + 11x + 12. If its length is (2x + 3) find the breadth.

Area of the rectangle = length × breadth

Given that the area of the rectangle is 2x² + 11x + 12 and breadth (2x + 3)

∴ Area of the rectangle = 2x² + 11x + 12 = length × (2x + 3)

Length = (2x² + 11x + 12) / (2x + 3)

= (2x² + 8x + 3x + 12) / (2x + 3)

= [2x(x + 4) + 3(x + 4)] / (2x + 3)

= [(2x + 3) (x + 4)] / (2x + 3)

= (x + 4)

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9

---

NCERT Exemplar Class 8 Maths Chapter 7 Problem 99

The area of a rectangle is x² + 7x + 12. If its breadth is (x + 3), then find its length.

Summary:

The area of a rectangle is x² + 7x + 12. If its breadth is (x + 3), then its length is (x + 4)

---

☛ Related Questions:

• The curved surface area of a cylinder is 2π (y² - 7y + 12) and its radius is (y - 3). Find the heigh . . . .
• The area of a circle is given by the expression πx² + 6πx + 9π. Find the radius of the circle
• The sum of first n natural numbers is given by the expression n²/2 + n/2. Factorise this expression