Respuesta :

MsRay

Answer:

length = 6 feet

width = 4 feet

Step-by-step explanation:

To find the dimensions of the rectangle, you can set up a variable and an expression that will equal the perimeter of the figure.  Given l = length, width is '8 feet less than twice the length' or w = 2l - 8.

The general formula for perimeter of a rectangle is:

2w + 2l = P, where w = width and l = length

Using the variable and expression from above and the perimeter of 20 feet:

2(2l - 8)+ 2l = 20

distribute: 4l - 16 + 2l = 20

combine like terms: 6l - 16 = 20

add 16 to both sides: 6l - 16 + 16 = 20 + 16 or 6l = 36

divide and solve for 'l':  6l/6 = 36/6, or l = 6 feet

solve for 'w':  w = 2(6) - 8 or w = 12 - 8 = 4 feet

Lanuel

The dimensions of the rectangular garden are 6 and 4 feet.

  • Let the length of the rectangular garden be L.
  • Let the width of the rectangular garden be W.

Given the following data:

  • Perimeter = 20 feet

Translating the word problem into an algebraic equation, we have;

[tex]W = 2L - 8[/tex]

To find the dimensions of the rectangular garden;

Mathematically, the perimeter of a rectangle is given by the formula;

[tex]Perimeter = 2(L + W)[/tex]

Substituting the values into the formula, we have;

[tex]20 = 2(L + 2L- 8)[/tex]

[tex]20 = 2(3L - 8)[/tex]

Opening the bracket, we have;

[tex]20 = 6L - 16[/tex]

[tex]6L = 20 + 16\\\\6L = 36\\\\L = \frac{36}{6}[/tex]

Length, L = 6 feet

Next, we would find the value of W;

[tex]W = 2L - 8[/tex]

Substituting the value of L, we have;

[tex]W = 2(6) - 8\\\\W = 12 - 8[/tex]

Width, W = 4 feet

Therefore, the dimensions of the rectangular garden are 6 and 4 feet.

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