The length of a rectangular field exceeds its breadth by $8 \mathrm{~m}$ and the area of the field is $240 \mathrm{~m}^{2}$. The breadth of the field is(a) $20 \mathrm{~m}$(b) $30 \mathrm{~m}$(c) $12 \mathrm{~m}$(d) $16 \mathrm{~m}$

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The length of a rectangular field exceeds its breadth by $8 \mathrm{~m}$ and the area of the field is $240 \mathrm{~m}^{2}$ . The breadth of the field is
(a) $20 \mathrm{~m}$
(b) $30 \mathrm{~m}$
(c) $12 \mathrm{~m}$
(d) $16 \mathrm{~m}$

The length of a rectangular field exceeds its breadth by $8 \mathrm{~m}$ and the area of the field is $240 \mathrm{~m}^{2}$ . The breadth of the field is
(a) $20 \mathrm{~m}$
(b) $30 \mathrm{~m}$
(c) $12 \mathrm{~m}$
(d) $16 \mathrm{~m}$

Let the breadth of the rectangular field be $x \mathrm{~m}$ .
$\therefore$ Length of the rectangular field $=(x+8) m$
Area of the rectangular field $=240 \mathrm{~m}^{2}$
$\therefore(x+8) \times x=240 \quad$ (Area=Length $\times$ Breadth) $\Rightarrow x^{2}+8 x-240=0$ $\Rightarrow x^{2}+20 x-12 x-240=0$ $\Rightarrow x(x+20)-12(x+20)=0$ $\Rightarrow(x+20)(x-12)=0$ $\Rightarrow x+20=0$ or $x-12=0$ $\Rightarrow x=-20$ or $x=12$
$\therefore x=12$ (Breadth cannot be negative)
Thus, the breadth of the field is $12 \mathrm{~m}$
Hence, the correct answer is option $\mathrm{C}$ .