A rectangular field has an area of $3 s q . u n i t s$ . The length is one unit more than twice the breadth. Frame an equation to represent this. [Assume breadth is $x$ ].

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

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$x^{2} - 2 x + 3 = 0$

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$2 x^{2} + x - 3 = 0$

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

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Solution

The correct option is A. $2 x^{2} + x - 3 = 0$
Let the breadth of the field be $x$ .
Given, length $= (2 \times b r e a d t h + 1)$ and area of the field is $3 s q . u n i t s$
$\Rightarrow$ Length of the field $= 2 x + 1$
$∵$ Area of rectangle = $length \times breadth$

$∴$ Area of the rectangular field $= x (2 x + 1)$
$\Rightarrow x (2 x + 1) = 3$
$\Rightarrow 2 x^{2} + x = 3$
$\Rightarrow 2 x^{2} + x - 3 = 0$
Hence, required equation is $2 x^{2} + x - 3 = 0$

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A rectangular field has an area of 3 sq. units. The length is one unit more than twice the breadth. Frame an equation to represent this. [Assume breadth is x].

A rectangular field has an area of $3 s q . u n i t s$ . The length is one unit more than twice the breadth. Frame an equation to represent this. [Assume breadth is $x$ ].