Question

the length of a rectangular lot is 6 less than twice its width if the area is 45 square cm what is the length and the width of the rectangle​

Answer 1

$\underline{\pink{ Dimensions \: of \: a \: rectangular \: plot : }}$

$Let \: the \: width (w) = x \: cm$

$Length (l) = (2x - 6 ) \: cm$

$Area \: of \: the \: plot (A) = 45 \: cm^{2} \:(given)$

$\implies l \times w = 45$

$\implies (2x-6)\times x - 45 = 0$

$\implies 2x^{2} - 6x - 45 = 0$

$Compare \: this \:with \: ax^{2} +bx+c = 0 ,\\we \:get$

$a = 2 , b = -6 , c = -45$

$Discriminant (D) = b^{2} - 4ac \\= (-6)-4\times 2 \times (-45) \\= 36 + 360 \\= 396$

/* Using Quadratic formula */

$x = \frac{ - b \pm \sqrt{D}}{2a }$

$=\frac{ -(-6) \pm \sqrt{396}}{2\times 2 } \\= \frac{6 \pm 6 \sqrt{11}}{4}\\= \frac{3\pm 3\sqrt{11}}{2}$

Therefore.,

$Breadth (w) = x = \frac{3+3\sqrt{11}}{2} \: cm$

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