The perimeter and length of a rectangle are in the ratio of 8 : 1, and the area of the rectangle is $$1323 cm^2$$. Find the length of the rectangle.

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

Given, Ratio of perimeter and length of the rectangle = 8 : 1

$$=$$>  $$\frac{2\left(l+b\right)}{l}=\frac{8}{1}$$

$$=$$>  $$\frac{l+b}{l}=\frac{4}{1}$$

$$=$$>  $$l+b=4l$$

$$=$$>  $$b=3l$$ ....................(1)

Area of the rectangle = $$1323 cm^2$$

$$=$$>  $$lb=1323$$

$$=$$>  $$l\left(3l\right)=1323$$

$$=$$>  $$3l^2=1323$$

$$=$$>  $$l^2=441$$

$$=$$>  $$l=21$$ cm

$$\therefore\ $$Length of the rectangle = 21 cm

Hence, the correct answer is Option B