Question

if the length of a rectangular park is 3 times the breadth. if the perimeter of the park is 192 m, find the dimensions of the park.

Answer 1

l=3b
perimeter=2(l+b)=192 m
here l=length of rectangle
b=width of rectangle
put l=3b
2(3b+b)=192m
2×4b=192m
b=192/8=24
l=3b=3×24= 72

Answer 2

Given :

• Length of park is 3 times the breadth.
• Perimeter of park is 192m.

To Find :

• Dimensions of Park.

Solution :

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

Length of the park is 3 times its breadth.So ,

$\longmapsto\tt{Length\:of\:Park=3x}$

$\longmapsto\tt{Perimeter=192m}$

Using Formula :

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

Putting Values :

$\longmapsto\tt{192=2(3x+x)}$

$\longmapsto\tt{\cancel\dfrac{192}{2}=3x+x}$

$\longmapsto\tt{96=4x}$

$\longmapsto\tt{x=\cancel\dfrac{96}{4}}$

$\longmapsto\tt\bold{x=24}$

So , The value of x is 24.

Now :

$\longmapsto\tt\bold{Breadth=24m}$

$\longmapsto\tt{Length=3(24)}$

$\longmapsto\tt\bold{72m}$

_______________________

VERIFICATION :

$\longmapsto\tt{192=2(l+b)}$

$\longmapsto\tt{192=2(72+24)}$

$\longmapsto\tt{192=2(96)}$

$\longmapsto\tt\bold{192=192}$

HENCE VERIFIED