Question

The length of a rectangular verandah is $3\text{m}$ more than its breadth. The numerical value of its area is equal to the numerical value of its perimeter. Taking $x$ as the breadth of the verandah, write an equation in $x$ that represents the above statement.

• A. $x^2-x-6=0$
• B. $x^2-x+6=0$
• C. $x^2-x+5=0$
• D. $x^2-x-5=0$

Answer 1

The correct option is A $x^2-x-6=0$

It is given that we have assumed $x$ as the breadth of the rectangular verandah.

So, the length of the verandah will be equal to $x+3$.

Area of the verandah $=$ Perimeter of verandah
$\Rightarrow l\times b=2(l+b)$
$\Rightarrow (3+x)\times x=2(3+x+x)$
$\Rightarrow 3x+x^2=2(3+2x)$
$\Rightarrow x^2+3x-6-4x=0$
$\Rightarrow x^2-x-6=0$