Question

The length of a rectangular field is $300m$ and breadth is $\frac{2}{3}$ its length. If a road of width $10m$ is built along the wall of the field, what is the area of the road.

Answer 1

Let $AB=300m$ be the length of the rectangular field $ABCD$.

Therefore, breadth $BC$ of the field $=\frac{2}{3}\times 300=200m$

Since, the with of the road is $10m$, therefore,

$\Rightarrow PQ=AB+2\times 10=300+20=320m$ and

$\Rightarrow QR=BC+2\times 10=200+20=220m$

Now, area of the road so constructed $=$ Area of rectangle $PQRS-$ Area of rectangle $ABCD$

$=320\times 220-300\times 200$

$=70400-60000$

$=10400m^2$