The length of a rectangle is twice the side of a square and its width is 6 m greater than the side of the square. If the area of the rectangle is three times the area of the square.

x^{2} - 12 x = 0

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x^{2} - 12 x + 6 = 0

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x^{2} - 12 x + 9 = 0

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x^{2} - 12 x + 10 = 0

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Solution

The correct option is A $x^{2} - 12 x = 0$
Let side of square $= x c m$
Therefore,
Length of rectangle $= 2 x$
Breadth of rectangle $= x + 6$
$2 x (x + 6) = 3 x^{2}$
$\Rightarrow 2 x^{2} + 12 x - 3 x^{2} = 0$
$\Rightarrow x^{2} + 12 x = 0$
$\Rightarrow x^{2} = 12 x$
$\Rightarrow x = 12$
Therefore,
Side of square $= 12 c m$
Length of rectangle $= 2 \times 12$
$= 24 c m$
Breadth of rectangle $= 12 + 6$
$= 18 c m$

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