Question

The length of a rectangle is 5 m less than four times its width. If the perimeter of the rectangle is 180 m, what is its area?​

Answer 1

Given :

• Length of a rectangle is 5 m less than four times its width/breadth .
• Perimeter of Rectangle is 180 m .

To Find :

• Area of Rectangle .

Solution :

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

As Given that Length of a rectangle is 5 m less than four times its width/breadth . So ,

$\longmapsto\tt{Length\:of\:Rectangle=4x-5}$

Using Formula :

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

Putting Values :

$\longmapsto\tt{180=2(4x-5+x)}$

$\longmapsto\tt{\cancel\dfrac{180}{2}=5x-5}$

$\longmapsto\tt{90+5=5x}$

$\longmapsto\tt{\cancel\dfrac{95}{5}=x}$

$\longmapsto\tt\bf{19=x}$

So , The value of x is 19 .

Therefore :

$\longmapsto\tt{Length=4(19)-5}$

$\longmapsto\tt\bf{71\:m}$

$\longmapsto\tt\bf{Width=71\:m}$

For Area of Rectangle :

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Rectangle=l\times{w}}$

Putting Values :

$\longmapsto\tt{71\times{19}}$

$\longmapsto\tt\bf{1349\:{m}^{2}}$

So, The Area of Rectangle is 1349 m² .

Answer 2

Question:-

• The length of a rectangle is 5 m less than four times its width. If the perimeter of the rectangle is 180 m, what is its area?

To Find:-

• Find the area.

Solution:-

Given ,

• Perimeter of rectangle is 180 m

• Length of rectangle is 4x - 5

• Breadth of rectangle is x

First ,

We have to find the value of length and breadth:-

$\dashrightarrow\sf \: Perimeter = 2( l + b )$

$\dashrightarrow\sf \: 180 = 2( 4x - 5 + x )$

$\dashrightarrow\sf \: 180 = 2( 5x - 5 )$

$\dashrightarrow\sf \:180 = 10x - 10$

$\dashrightarrow\sf \: 10x = 180 + 10$

$\dashrightarrow\sf \: 10x = 190$

$\dashrightarrow\sf \: x = \cancel\dfrac { 190 } { 10 }$

$\dashrightarrow\sf \: x = 19$

Hence ,

• Breadth is 19 m.

• Length is 4x - 5 = 71 m.

Now ,

We have to find the area:-

$\dashrightarrow\sf \: Area = length \times breadth$

$\dashrightarrow\sf \: Area = 71 \times 19$

$\dashrightarrow\sf \: Area = 1349 \: { m }^{ 2 }$

Hence ,

• Area is 1349 m²