Respuesta :

Let x be the width
width = x

Length is twice its width
length = 2x

Perimeter = length + width + length + width
Perimeter = x + 2x + x + 2x = 6x

Given that perimeter = 7 1/3
6x = 7 1/3 
x = 7 1/3 ÷ 6 = 1 2/9

So width = 1 2/9
Length = 1 2/9 x 2 = 2 4/9

Area = length x width
Area = 1 2/9 x 2 4/9
Area = 2 80/81 square cm

The area of the rectangle is 242/81 cm and this can be determined by using the formula of the area and perimeter of the rectangle.

Given :

  • The length of a rectangle is twice its width.
  • The perimeter of a rectangle is 7 1/3 cm.

The following steps can be used in order to determine the area of the rectangle:

Step 1 - The formula of the perimeter of the rectangle is given below:

[tex]\rm P = 2(L + W)[/tex]    --- (1)

where W is the width and L is the length of the rectangle.

Step 2 - According to the given data, the length of a rectangle is twice its width, that is:

L = 2W    --- (2)

Step 3 - Now, substitute the values of the known terms in the expression (1).

[tex]\rm \dfrac{22}{3} = 2(2W+W)[/tex]

[tex]\rm \dfrac{22}{3}=6W[/tex]

[tex]\rm W = \dfrac{11}{9} \; cm[/tex]

Step 4 - Now, substitute the value of 'W' in expression (2).

[tex]\rm L = \dfrac{22}{9}[/tex]

Step 5 - Now, the area of the rectangle is given below:

[tex]\rm A = \dfrac{11}{9}\times \dfrac{22}{9}[/tex]

[tex]\rm A = \dfrac{242}{81} \; cm[/tex]

For more information, refer to the link given below:

https://brainly.com/question/2142493

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