Question

The length of a rectangular plot is 2 m more than thrice its breadth. The area of the plot is 1240 m${}^2$. Find its length and breadth (approximate the values).

• A. 62 m and 20 m
• B. 88 m and 24 m
• C. 32.6 m and 16.3 m
• D. 44.6 m and 14.20 m

Answer 1

The correct option is A

62 m and 20 m

Let x and y be the length and breadth of the rectangle respectively.

Given, x = 2+3y

Area of the rectangle = length $\times$ breadth = $xy$

$(2+3y)y=1240$
$2y+3y^2=1240$
$3y^2+2y-1240=0$

$\Rightarrow a=3,b=2,c=-1240$

$\Rightarrow b^2-4ac=4-4\left(3\right)(-1240)$

$\Rightarrow b^2-4ac=14884$

$\Rightarrow \sqrt{b^2-4ac}=122$

$\Rightarrow x=\frac{-2-122}{6},\frac{-2+122}{6}$
we get, $x=-20.67,20$.

Since breadth cannot be negative, breadth = 20 m and length = 62 m.