Question

Perimeter of rectangular park is $450m.$ The lengths of the sides are in ratio $3:2$.Find the area of the rectangle

Answer 1

Let the ratio constant be $x$.

Let the length be $3x$ and breadth be $2x$.

Perimeter of rectangle $=$$450m$

$\begin{array}{rcl}2(l+b)& =& 450\\ 3x+2x& =& \frac{450}{2}\\ 5x& =& 225\\ x& =& \frac{225}{5}\\ x& =& 45\end{array}$

$\therefore$Length of rectangle $=3x=3\times 45=135m$

Breadth of rectangle $=2x=2\times 45=90m$

Area of the rectangle $=l\times b$

$$\begin{gathered} =135\times 90 \\ =12,150m^2 \end{gathered}$$

Thus, the area of the rectangle is $12,150m^2$.