Question

Rahul purchased a rectangular plot of area $634{\text{m}}^2$. If the length of the plot is 2 m more than thrice its breadth, then find the length and breadth of the given plot.

Answer 1

Let, the length of the given plot be $x$ m and breadth be $y$ m.

Given,
Area of the rectangular plot = $634{\text{m}}^2$
and its length is 2 m more than thrice its breadth, which implies $x=3y+2$.

We know,
$\text{Area of the rectangle}=\text{length}\times \text{breadth}$
$\therefore 634=xy\Rightarrow 634=(2+3y)y\Rightarrow 634=2y+3y^2\therefore 3y^2+2y-634=0$

This equation resembles the general form of quadratic equation $a{x}^2+bx+c=0.$

Lets find the values of $y$ satisfying the equation. (Roots of the equation)

$y=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{-2\pm \sqrt{2^2-4\times 3(-634)}}{2\times 3}y=\frac{-2\pm \sqrt{4+7608}}{6}=\frac{-2\pm \sqrt{7612}}{6}y=\frac{-2\pm 87.246}{6}y=\frac{-2+87.246}{6}\text{or}\frac{-2-87.246}{6}y=14.20\text{or}-14.87$

Length is always positive.
$\therefore y=14.20\text{m}$

$x=2+3y\therefore x=2+3\left(14.20\right)=44.6\text{m}$

Hence, the length of the given rectangular plot is $44.6\text{m}$ and its breadth is $=14.2\text{m}$.