Question

100 points please help

The school designed their vegetable garden to have a perimeter of 32 feet with the length measuring two feet more than twice the width.

Using l to represent the length of the garden and w to represent its width, write and solve a system of equations that describes this situation.
Perimeter- ______ L+________ W= _________
Length compared to width- L= ______ W+ _________

Answer 1

We can set up two equations to describe the situation:

Perimeter: 2L + 2W = 32

Length compared to width: L = 2W + 2

Solving for W in equation 2 and substituting into equation 1, we get:

L = 2W + 2

2L + 2W = 32

Substituting L = 2W + 2:

2(2W + 2) + 2W = 32

4W + 4 + 2W = 32

6W + 4 = 32

6W = 28

W = 4.67

So the width of the garden is approximately 4.67 feet. To find the length, we can substitute this back into equation 2:

L = 2W + 2

L = 2(4.67) + 2

L = 9.34 + 2

L = 11.34

So the length of the garden is approximately 11.34 feet.