Question

The length and breadth of a rectangular field are in the ratio 5 : 3 and its perimeter is 480 m.
The area of the field is

(a) 7200 m² (b) 13500 m² (c) 15000 m² (d) 54000 m²

Answer 1

Let l = 5x and b = 3x be the length and breadth of the rectangular field. Here, perimeter = 480 m.
So, as per the question
Perimeter = 2 (l + b)
$$\begin{gathered} \Rightarrow 480=2\left(5x+3x\right) \\ \Rightarrow 16x=480 \\ \Rightarrow x=30 \end{gathered}$$
l = 5 $\text{×}$ 30 = 150 m
b = 3 $\text{×}$ 30 = 90 m
Now
Area of the rectangular filed = l $\text{×}$ b = 150 $\text{×}$ 90 = 13500 m²
Hence, the correct option is (b).