The perimeter of a rectangular field is 480 m. The ratio between the length and the breadth of the field is 2 : 1. Find the area of the field.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 12,800 m2
The perimeter of a rectangle is \(2(l+b)\), so half of it gives the sum of the length and the breadth. The ratio 2 : 1 then splits this sum into 3 equal parts, two for the length and one for the breadth.
Length plus breadth: \(l+b=\displaystyle\frac{480}{2}=240\,\mathrm{m}\)
Length is two parts out of three: \(\displaystyle\frac{2}{3}\times240=160\,\mathrm{m}\)
Breadth is one part out of three: \(\displaystyle\frac{1}{3}\times240=80\,\mathrm{m}\)
Area of the field: \(160\times80=12800\,\mathrm{m^2}\)