Question

The perimeter of Dana's rectangular garden is 42 feet. The length of her garden is 6 feet more than twice the width.

Answer 1

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

Answer 2

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;

$l = 2w + 6$

Furthermore, the perimeter is 42 feet

The formula of the perimeter is;

$2(l + w) = 42$

Dividing both sides by 2

$l + w = 21$

c)Now, we want to solve both equations simultaneously

We can substitute the first equation into the second;

$2w + 6 + w = 21 \\ 3w + 6 = 21 \\ 3w = 21 - 6 \\ 3w = 15 \\ w = \frac{15}{3} = 5$

$l + w = 21 \\ l = 21 - w = 21 - 5 = 16$