Question

The width of a rectangle is two-thirds of its length. If the perimeter of the rectangle is 80m.find it area

Answer 1

Answer:

384 sq. m

Step-by-step explanation:

Given that,

The width of a rectangle is two-thirds of its length.

Let the length be l.

Therefore, we will get,

The width will be = 2l/3

Also, it's given that,

Perimeter = 80 m

But, we know that,

p = 2(length + width)

Therefore, we will get,

=> 2(l + 2l/3) = 80

=> (3l+2l)/3 = 80/2

=> 5l/3 = 40

=> l = 40 × 3/5

=> l = 8 × 3

=> l = 24

Therefore, we will get,

=> Width = 2 × 24/3

=> Width = 16

Therefore, the length and the width is 24 m and 16 m respectively.

Now, we know that,

Area = length × width

=> Area = 24×16

=> Area = 384

Hence, the required area is 384 sq. m

Answer 2

Given that ,

• The perimeter of rectangle is 80 m

• The width of a rectangle is two-thirds of its length

Let ,

The length of rectangle be " x "

Then , width of rectangle = 2x/3

We know that , the perimeter of rectangle is given by

$\large \sf\fbox{Perimeter = 2(l + b) }$

Thus ,

80 = 2(x + 2x/3)

40 = (3x + 2x)/3

120 = 5x

x = 24

$\sf \therefore \underline{The \: length \: and \: width \: of \: rectangle \: are \: 24 \: m \: and \: 16 \: m}$

Now , the area of rectangle is given by

$\large \sf\fbox{Area = l × b}$

Thus ,

Area = 24 × 16

Area = 384 m²

$\sf \therefore \underline{The \: area \: of \: rectangle \: is \: 384 \: sq. \: m }$