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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

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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,
Length × Breadth = Area

\[x(1 + 2x) = 528\]

\[ \Rightarrow 2 x^2 + x - 528 = 0\]

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

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

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

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

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

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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