Question

Solve the equation obtained $x^2-x-6=0$ and hence find the dimensions of the verandah. Verandah is in rectangular shape having area and perimeter equal.

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

Answer 1

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

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