Question

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

• A. length $=40,$ breath $=16$
• B. length $=25,$ breath $=12$
• C. length $=48,$ breath $=16$
• D. length $=32,$ breath $=20$

Answer 1

The correct option is A length $=40,$ breath $=16$

Let length$=5x$; Breadth$=2x$

(Image)

Area of path$=(5x+5)(2x+5)-\left(5x\right)\left(2x\right)$

$\Rightarrow 10x^2+25x+10x+25-10x^2=305$

$\Rightarrow 35x+25=305$

$x=\frac{305-25}{35}=8$

Length$=40m\left(5x\right)$

Breadth$=16m\left(2x\right)$