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The breadth of a rectangular field is 60% of its length. If the perimeter of the field is 800 m, find out the area of the field.

37500 m2
30500 m2
32500 m2
40000 m2
Explanation:

Given that breadth of a rectangular field is 60% of its length

$\Rightarrow b = \dfrac{60l}{100} = \dfrac{3l}{5}$

perimeter of the field = 800 m

=> 2 (l + b) = 800

$\Rightarrow 2\left(l + \dfrac{3l}{5} \right)=800$

$\Rightarrow l + \dfrac{3l}{5} = 400$

$\Rightarrow \dfrac{8l}{5} = 400$

$\Rightarrow \dfrac{l}{5} = 50$

$\Rightarrow l = 5 \times 50 = 250\text{ m}$

$\text{b = }\dfrac{3l}{5} = \dfrac{3 \times 250}{5} = 3 \times 50 = 150\text{ m}$

Area = $\text{lb = }250 \times 150 = 37500\text{ m}^2$

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