Question

A fence was installed around the edge of a rectangular garden. The length. I, of the fence was 5 feet less than 3 times its width. w. The amount of fencing used was 90 feet. Write a system of equations or write an equation using one variable that models this situation.

Determine algebraically the dimensions, in feet, of the garden.

Answer 1

Width: w = 12.5 feet

Length: L = 32.5 feet

Explanation:

Let's use two variables to represent the dimensions of the rectangular garden:

Let w be the width of the garden (in feet)

Let L be the length of the garden (in feet)

The problem tells us that the length of the fence is 90 feet, so we can write the equation:

2L + 2w = 90

We also know that the length of the fence (L) is 5 feet less than 3 times the width (w). We can write this as another equation:

L = 3w - 5

Now we have two equations with two variables. We can solve this system of equations using substitution or elimination.

Let's use substitution:

Substitute the expression for L in terms of w from the second equation into the first equation:

2(3w - 5) + 2w = 90

Simplify and solve for w:

6w - 10 + 2w = 90

8w = 100

w = 12.5

Now we can use this value of w to find L:

L = 3w - 5 = 3(12.5) - 5 = 32.5

Therefore, the dimensions of the rectangular garden are as follows:

Width: w = 12.5 feet

Length: L = 32.5 feet