Question

The perimeter of a rectangular plot is $48$ m and its area is $108m^2$. The dimensions of the plot are

• A. $12$ and $9$
• B. $18$ and $6$
• C. $27$ and $4$
• D. $36$ and $3$

Answer 1

Answer: (B)

$18$ and $6$

Let dimensions of a rectangular plot are $x$ and $y$ m.
By hypothesis $2(x+y)=48$
or $x+y=24$ ...(i)
and $xy=108$ ...(ii)
From equation (i) $y=24-x$
Substituting the value of $y$ in equation (ii), we get
$x(24-x)=108$
$24x-x^2=108$
$x^2-24x+108=0$
$x^2-18x-6x+108=0$
or $x(x-18)-6(x-18)=0$
or $(x-18)(x-6)=0$
If $x=18$, then $y=24-18=6$
and if $x=6$, then $y=24-6=18$
Hence, the dimensions are 18m and 6m.