Question

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

Taking $x$ as the breath of the verandah, write an equation in $x$ that represents the above statement.

• A. $x^2-x-6=0$
• B. $x^2-x-8=0$
• C. $3x^2-x-6=0$
• D. $2x^2-x-6=0$

Answer 1

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

Let the breadth of rectangular verandah $=xm$

Therefore,
Length = $x+3$............[According to given statement]

Area of the verandah $=$ Perimeter of the verandah

$=>l\times b=2(l+b)$

$=>(3+x)\times x=2(3+x+x)$

$=>3x+x^2=2(3+2x)$

$=>x^2+3x-6-4x=0$

$=>x^2-x-6=0$