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The perimeter of Dana's rectangular garden is 42 feet. The length of her garden is 6 feet more than twice the width.
A. Define the variables. (1pt)
B. Create an equation(s) that can be used to determine the length and width of the garden. (1pt)
C. What is the length and width of the garden? Show all your work (1pt)

Respuesta :

mhanifa

Answer:

  • The length is 16 feet, the width is 5 feet

Step-by-step explanation:

Given:

  • The perimeter of the rectangular garden is 42 feet
  • The length is 6 feet more than twice the width

A. The variables are:

  • The length - l
  • The width - w

B. The equations are based on given parameters

Use perimeter formula

  • 2(l + w) = 42
  • l = 2w + 6

C. Solve the system above by substitution:

  • 2(l + w) = 42
  • l + w = 21
  • 2w + 6 + w = 21
  • 3w = 15
  • w = 5

Find the value of l:

  • l = 2*5 + 6 = 16

The length is 16 feet, the width is 5 feet

DarlinEsteves

Answer:

The length of the garden is 16 ft while the width of the garden is 5 ft.

Explanation:

a)we want to start with defining the variables.

Let the length of the garden be w.

b) here, we want to create equation

From the question, the length is 6 feet more than twice the width of one garden

Mathematically, we have this as;

[tex]l = 2w + 6[/tex]

Furthermore, the perimeter is 42 feet

The formula of the perimeter is;

[tex]2(l + w) = 42[/tex]

Dividing both sides by 2

[tex]l + w = 21[/tex]

c)Now, we want to solve both equations simultaneously

We can substitute the first equation into the second;

[tex]2w + 6 + w = 21 \\ 3w + 6 = 21 \\ 3w = 21 - 6 \\ 3w = 15 \\ w = \frac{15}{3} = 5[/tex]

[tex]l + w = 21 \\ l = 21 - w = 21 - 5 = 16[/tex]

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