Question

The length of a rectangle exceeds its breadth by 3 cm If the numerical values of the area and the perimeter of the rectangle are equal then the breadth of a rectangle will be

• A. 2 cm
• B. 3 cm
• C. 1 cm
• D. 5 cm

Answer 1

The correct option is B 3 cm

Let the breadth of rectangle is x cm ,then length is x+3

Then the area of rectangle =x(x+3)

And perimeter of rectangle =2(x+3+x)

As per question area and perimeter numerical equal

$\therefore X(x+3)=2(x+3+x)$

$\Rightarrow x^2+3x=4x+6$

$\Rightarrow x^2+3x-4x-6=0$

$\Rightarrow x^2-x-6=0$

$\Rightarrow x^2-3x+2x-6=0$

$\Rightarrow x^{(}x-3)+2(x-3)=0$

$\Rightarrow (x-3)(x+2)=0$

So x=3 or x=-2 But -2 not the write because breadth no negative

Then breadth=3 cm