Question

The length of a rectangle is three times its breadth if the breadth is decreased by 2 m and breadth increased by 4 m the area of the rectangle is decreased by 1/3

a) form a quadratic equation ​

Answer 1

Let the breadth is x, then the length is 3x.

The area is:

• A = lw = 3x*x = 3x²

The breadth is decreased by 2 m:

• w = x - 2

The length is increased by 4m:

• l = 3x + 4

The area is now:

• (x - 2)(3x + 4) = 3x² - 1/3(3x²)
• 3x² + 4x - 6x - 8 = 2x²
• x² - 2x - 8 = 0
• x² - 2x + 1 = 9
• (x - 1)² = 3²
• x - 1 = 3
• x = 4

The breadth was 4 m and the length 12 m