Question

The length and breadth of a rectangular park are in the ratio $5:2$ . A $2.5$ m wide path running all round the out side of the park has an area $305m^2$. Find the dimensions of the park.

Answer 1

R.E.F image

The ratio of length and breadth

of the rectangular park is $5:2$

$\therefore$ length $=5x$ m

breadth $=2x$ m

$\Rightarrow$ Area of the park = $5x.2x{m}^2$

$=10x^2{m}^2$

A $2.5$ wide path is made outside the park

$\therefore$ outer length of the park $=(5x+2.5+2.5)$ m

$=(5x+5)$ m

outer breadth of the park $=(2x+2.5+2.5)$ m

$=(2x+5)$ m

$\therefore$ Area of the park including the path $=(5x+5)(2x-5)$

$=10x^2+25x+10x+25m^2$

$=10x^2+35x+25m^2$

$\therefore$ Area of the path $=[10x^2+35x+25-10x^2]m^2$

$=[35x+25]m^2$

But, given area of path $=305$ $m^2$

$\Rightarrow 35x+25=305$

$\Rightarrow 35x=305-25$

$\Rightarrow \frac{280}{35}=8$

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

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