Question

The length and breadth of a rectangular park are in the ratio 3 :1. A 1m wide path runs through the inside of the park and has an area of 39 sq. m. Find the length and breadth of the park.

Answer 1

Let length be $3x$ and breadth be $x$.

Area of path $=(3x+2)(x+2)-(3x\times x)$

$\Rightarrow {3x}^2+6x+2x+4-{3x}^2=39$

$\Rightarrow 8x=39-4=35$

$\Rightarrow x=\frac{35}{8}=4.375m$

Length $=3\times 4.375=13.125m$

Breadth $=4.375m$