Answer :

**Given: **The area of a rectangular plot is 528 m^{2}. 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 m^{2}

⇒ a × (2a + 1) = 528

⇒ 2a^{2} + 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.

⇒ 2a^{2} + 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

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