If the perimeter and length of a rectangle are in the ratio 6:1 and the area of the rectangle is 288 cm$$^2$$. Find the length of the rectangle.

Let the length and breadth of the rectangle are l and b respectively.

Ratio of perimeter and length of the rectangle = 6:1

$$\Rightarrow$$  $$\frac{2\left(l+b\right)}{l}=\frac{6}{1}$$

$$\Rightarrow$$  $$2l+2b=6l$$

$$\Rightarrow$$  $$2b=4l$$

$$\Rightarrow$$  $$b=2l$$

Area of the rectangle = 288 cm$$^2$$

$$\Rightarrow$$  $$lb=288$$

$$\Rightarrow$$  $$l\left(2l\right)=288$$

$$\Rightarrow$$  $$2l^2=288$$

$$\Rightarrow$$  $$l^2=144$$

$$\Rightarrow$$  $$l=12$$ cm

$$\therefore\ $$Length of the rectangle = 12 cm

Hence, the correct answer is Option A