Question

The area of a rectangular plot is $528m^2$. The length of the plot (in metres) is one more than twice its breadth. Find the length and breadth of the plot.

• A. Length is $31$ m and breadth is $12$ m
• B. Length is $32$ m and breadth is $14$ m
• C. Length is $33$ m and breadth is $16$ m
• D. Length is $34$ m and breadth is $18$ m

Answer 1

The correct option is C Length is $33$ m and breadth is $16$ m

Let the breath of the rectangle be $x$ m

Thus, length of the rectangle $=(2x+1)$ m

Area of a rectangle $=$ Length $\times$ breath

Thus $x(2x+1)=528$

$\Rightarrow 2x^2+x-528=0$
$\Rightarrow 2x^2+33x-32x-528=0$
$\Rightarrow x(2x+33)-16(2x+33)=0$
$\Rightarrow (2x+33)(x-16)=0$

Thus, $2x+33=0$ or $x-16=0$

$\Rightarrow x=\frac{-33}{2}$ or $x=16$

Now, breath of a rectangle cannot be negative.
Thus, $x=-\frac{33}{2}$ is not possible.

Therefore, breath of the rectangle is $16$ m and length of the rectangle is $(2\times 16+1)=33$ m.