Question

The width of a rectangular garden is two thirds of its length. If its perimeter is 40 m, find the width.

Answer 1

Answer:

let length be x and breadth be y

A/Q,

$= > y = \frac{2}{3} x \\ \\ and \\ \\ perimeter = 40 \: m \\ = > 2(x + y) = 40 \\ = > 2(x + \frac{2}{3} x) = 40 \\ = > \frac{5}{3} x = 20 \\ = > x = 12 \: m \\ \\ then \\ = > y = \frac{2}{3}x \\ = > y = \frac{2}{ 3} \times 12 \\ = > y= 8\: m$

therefore

length = 12 m

width = 8 m

Answer 2

Given :

• Width of Rectangular garden is two third of its length.
• Perimeter of Rectangle = 40m

To Find :

• Width of Rectangle.

Solution :

$\longmapsto\tt{Let\:length\:be=x}$

If Width of the rectangular garden is two third of its length. So ,

$\longmapsto\tt{Width=\dfrac{2x}{3}}$

Using Formula :

$\longmapsto\tt\boxed{Perimeter\:of\:Rectangle=2(l+b)}$

Putting Values :

$\longmapsto\tt{40=2\dfrac{x}{1}+\dfrac{2x}{3}}$

$\longmapsto\tt{\cancel\dfrac{40}{2}=\dfrac{x}{1}+\dfrac{2x}{3}}$

$\longmapsto\tt{20=\dfrac{3x+2x}{3}}$

$\longmapsto\tt{20=\dfrac{5x}{3}}$

$\longmapsto\tt{x=\dfrac{\cancel{20}\times{3}}{\cancel{5}}}$

$\longmapsto\tt{x=4\times{3}}$

$\longmapsto\tt\bold{x=12}$

Value of x is 12..

Therefore :

$\longmapsto\tt\bold{Length=12m}$

$\longmapsto\tt{Width=\dfrac{2}{\cancel{3}}\times{\cancel{12}}}$

$\longmapsto\tt{4\times{2}}$

$\longmapsto\tt\bold{8m}$

_______________________

VERIFICATION :

$\longmapsto\tt{40=2(l+b)}$

$\longmapsto\tt{40=2(12+8)}$

$\longmapsto\tt{40=2(20)}$

$\longmapsto\tt\bold{40=40}$

HENCE VERIFIED