The area of a rectangular plot is 528 m². The length of the plot (in metres) is one metre more then twice its breadth. Find the length and the breadth of the plot. (CBSE 2014)

Given: The area of a rectangular plot is 528 m². The length of the plot (in metres) is one metre more then twice its breadth. 

To find: the length and the breadth of the plot.

Solution:

Let the breadth be ‘a’ m

Given, length of the plot (in metres) is one metre more then twice its breadth.

⇒ length = (2a + 1) m

Now, area of a rectangular plot is 528 m²

⇒ a × (2a + 1) = 528

⇒ 2a² + a – 528 = 0

In factorization, we write the middle term of the quadratic equation either as a sum of two numbers or difference of two numbers such that the equation can be factorized.

⇒ 2a² + 33a – 32a – 528 = 0

⇒ a(2a + 33) – 16(2a + 33) = 0

⇒ (2a + 33)(a – 16) = 0

⇒ (2a + 33) = 0 and (a – 16) = 0

⇒ 2a = -33 and a = 16

⇒ a = -33/2 and a = 16

⇒ a = 16 m

length = (2a + 1) = 2 × 16 + 1 = 33 m

Hence breadth = 16 m and length = 33 m