Question

The length of a rectangular verandah is $3m$ more than its breadth. The numerical value of its area is equal to the numerical value of its perimeter. Find the dimensions of the verandah.

• A. $x=6$; length $=5m$ and breadth $=3m$
• B. $x=3$; length $=6m$ and breadth $=3m$
• C. $x=4$; length $=4m$ and breadth $=2m$
• D. $x=5$; length $=7m$ and breadth $=2m$

Answer 1

The correct option is B $x=3$; length $=6m$ and breadth $=3m$

Let the breadth of rectangular verandah $=$ $x$
Therefore, length $=$ $x+3$ [According to given statement]
Area of the verandah $=$ Perimeter of verandah
$\Rightarrow l\times b=2(l+b)$
$\Rightarrow (3+x)\times x=2(3+x+x)$
$\Rightarrow 3x+x^2=2(3+2x)$
$\Rightarrow x^2+3x-6-4x=0$
$\Rightarrow x^2-x-6=0$
$\Rightarrow x^2-3x+2x-6=0$
$\Rightarrow x(x-3)+2(x-3)=0$
$\Rightarrow (x-3)(x+2)=0$
$\Rightarrow x=3,x=-2$
Now, $x\ne -2$, as dimension of the verandah cannot be in negative,
Therefore, $x=3$
Length of rectangle $=$ $x+3$
$=$ $3+3$
$=$ $6m$
Breadth of rectangle $=$ $x$
$=$ $3m$