**Question:**

The width of a rectangle is two-thirds its length. If the perimeter is 180 metres, find the dimensions of the rectangle.

**Solution:**

Let the width of the rectangle be $x \mathrm{~cm}$.

It is $\frac{2}{3}$ of the length of the rectangle.

This means that the length of the rectangle will be $\frac{3}{2} x$.

Perimeter of the rectangle $=2(x)+2\left(\frac{3}{2}\right) x=180 \mathrm{~m}$

$\therefore 2 x+\frac{6 x}{2}=180$

$\Rightarrow \frac{4 x+6 x}{2}=180 \quad$ (taking the L. C.M. of 1 on the L.H.S. of the equation)

$\Rightarrow 10 x=2 \times 180 \quad$ (by cross multiplication)

$\Rightarrow 10 x=360$

$\Rightarrow x=\frac{360}{10}=36$

Therefore, the width of the rectangle is $36 \mathrm{~m}$.

Length of the rectangle will be $=\frac{3}{2} \mathrm{x}=\frac{3}{2}(36)=54 \mathrm{~m}$