The width of Sudha’s garden is $\frac{2}{3}$of its length. If its perimeter is 40 m, find its dimensions. 

Given, Perimeter = 40 m 

Let the length of the garden be x m. 

Then the width of the garden =$\frac{2}{3}x$ m. 

Perimeter = 2(length + width) 

$$\therefore 2\left(x+\frac{2}{3}x\right)=40$$ 

$$\Rightarrow 2x+\frac{4x}{3}=40$$ 

$$\Rightarrow 6x+4x=120$$ 

$$\Rightarrow 10x=120$$ 

$$\Rightarrow x=12$$ 

And, $\frac{2}{3}x$ =$\frac{2}{3}\times 12$ = 8 

Hence, the required length and width of Sudha’s garden is 12 m and 8 m respectively.