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Home » The perimeter of a rectangular plot is and its area is 288 sq meters. Find the dimension of the plot
The perimeter of a rectangular plot is 62 \mathrm{~m} and its area is 288 sq meters. Find the dimension of the plot
CBSE | Class 10 | Exercise 10e | Maths | Quadratic Equations | RS Aggarwal
The perimeter of a rectangular plot is 62 \mathrm{~m} and its area is 288 sq meters. Find the dimension of the plot

Let the length and breadth of the rectangular plot be x and y meter, respectively.

Therefore, we have:

\begin{array}{l} \text { Perimeter }=2(x+y)=62 \quad \ldots . .(i) \text { and } \\ \text { Area }=x y=228 \\ \Rightarrow y=\frac{228}{x} \end{array}

Putting the value of y in (i), we get

\begin{array}{l} \Rightarrow 2\left(x+\frac{228}{x}\right)=62 \\ \Rightarrow x+\frac{228}{x}=31 \\ \Rightarrow \frac{x^{2}+228}{x}=31 \\ \Rightarrow x^{2}+228=31 x \\ \Rightarrow x^{2}-31 x+228=0 \\ \Rightarrow x^{2}-(19+12) x+228=0 \\ \Rightarrow x^{2}-19 x-12 x+228=0 \\ \Rightarrow x(x-19)-12(x-19)=0 \\ \Rightarrow(x-19)(x-12)=0 \\ \Rightarrow x=19 \text { or } x=12 \end{array}

If x=19 m, y=\frac{228}{19}=12 \mathrm{~m}

Therefore, the length and breadth of the plot are 19 \mathrm{~m} and 12 \mathrm{~m}, respectively.

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