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Home » The length of a rectangle is thrice as long as the side of a square. The side of the square is more than the width of the rectangle. Their areas being equal, find the dimensions.
The length of a rectangle is thrice as long as the side of a square. The side of the square is 4 \mathrm{~cm} more than the width of the rectangle. Their areas being equal, find the dimensions.
CBSE | Class 10 | Exercise 10e | Maths | Quadratic Equations | RS Aggarwal
The length of a rectangle is thrice as long as the side of a square. The side of the square is 4 \mathrm{~cm} more than the width of the rectangle. Their areas being equal, find the dimensions.

Let the breadth of rectangle be x \mathrm{~cm}.

According to the question:

Side of the square =(x+4) \mathrm{cm}

Length of the rectangle =\{3(x+4)\} \mathrm{cm}

It is given that the areas of the rectangle and square are same.

\begin{array}{l} \therefore 3(x+4) \times x=(x+4)^{2} \\ \Rightarrow 3 x^{2}+12 x=(x+4)^{2} \\ \Rightarrow 3 x^{2}+12 x=x^{2}+8 x+16 \\ \Rightarrow 2 x^{2}+4 x-16=0 \\ \Rightarrow x^{2}+2 x-8=0 \\ \Rightarrow x^{2}+(4-2) x-8=0 \\ \Rightarrow x^{2}+4 x-2 x-8=0 \\ \Rightarrow x(x+4)-2(x+4)=0 \\ \Rightarrow(x+4)(x-2)=0 \\ \Rightarrow x=-4 \text { or } x=2 \\ \therefore x=2 \quad \text { ( } x \text { 'The value of } x \text { cannot be negative) } \end{array}

Thus, the breadth of the rectangle is 2 \mathrm{~cm} and length is \{3(2+4)=18\} \mathrm{cm}. Also, the side of the square is 6 \mathrm{~cm} .

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