Question

The length and breadth of a rectangular park are in ratio of $5:2$ a 2.5 m wide path running all around the outside of the park has an area of $305m^2$. find the dimensions of the park

Answer 1

Let the length of the park$=5a$ and its breadth $=2a$

$\therefore$ Area of the rectangular park$=5a\times 2a=10a^2$

Width of the park$=2.5$

Outer length $PQ=5a+2.5+2.5=5a+5$

Outer length $QR=2a+2.5+2.5=2a+5$

Area of $PQRS=(5a+5)(2a+5)=10a^2+35a+25$

Area of the path$=10a^2+35a+25-10a^2$

$\Rightarrow 305=35a+25$

$\Rightarrow 35a=305-25=280$

$\therefore a=\frac{280}{35}=8$

$\therefore$ Length of the park$=5a=5\times 8=40$m

Breadth of the park$=2a=2\times 8=16$m