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# 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 Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Completing the Square

#### Question

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.

#### Solution

Let the breadth of the rectangular plot be m.
Then, the length of the rectangular plot = (1 + 2x) m.
According to the question,

$x(1 + 2x) = 528$

$\Rightarrow 2 x^2 + x - 528 = 0$

$\Rightarrow 2 x^2 + 33x - 32x - 528 = 0$

$\Rightarrow x(2x + 33) - 16(2x + 33) = 0$

$\Rightarrow (x - 16)(2x + 33) = 0$

$\Rightarrow x - 16 = 0 \text { or } 2x + 33 = 0$

$\Rightarrow x = 16 \text { or } x = - \frac{33}{2}$

Since, length and breadth of the rectangle cannot be negative.
Thus, the breadth of the rectangular plot is 16 m.
and the length of the rectangular plot is (1 + 2×16) = 33 m.

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Solution 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. Concept: Solutions of Quadratic Equations by Completing the Square.
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