a rectangular garden is fenced on all sides with 256 feet of fencing. the garden is 8 feet longer than its wide. find the length and width of the garden. what is the equation

Answer 1

Definitely looks like a simultaneous-equations problem (two equations, two unknowns).

You are given two conditions involving the dimensions (length L and width W) of the rectangle:

1.      The total perimeter is 256 feet, and

2.      The garden is 8 feet longer than it is wide.

Translate these into equations, solve for L and W, and you’re there!

1)     Total perimeter is 256 feet

Write an equation equating the total distance around the rectangle to 256 feet:

Perimeter = L + W + L + W = 256

or

2L + 2W = 256

We can simplify a bit by dividing through by 2:

L + W = 128

2)     Garden is 8 feet longer than it is wide

Easy.

L = W + 8

We can solve this extremely system in multiple ways.

The most obvious and straightforward method is substitution, where we substitute one variable in terms of the other, and solve.

In this case, the substitution is handed to us, ready-made!

(You often have to work to get one of the equations into substitution-ready form… that’s probably what’s coming next… shhhh…. :) )

Substitute in the second equation into the first, and solve:

L + W = 128

(W + 8) + W = 128

2W + 8 = 128

2W = 120

W = 60

Now that we have the length, use the other equation to find the width:

L = W + 8

= 60 + 8

= 68

So the length of the garden is 68 feet, and the width is 60 feet.

Let’s check our answer in the original equation (ALWAYS STRONGLY SUGGESTED):

2L + 2W = 256

2(68) + 2(60) = 256

2 56 = 256

It works!

Answer 2

I hope this helps!

Answer 3

It may help to draw a picture. Draw a rectangle and label the sides W and L.

we know that the length is 8 feet longer than the width. This can be expressed as:

L= W + 8

we are also given that 256 feet of fencing was used. This equals our perimeter. The formula for the perimeter is:

P = 2* L + 2*W

256 = 2L + 2W

we can sub in our other equation for L:

256 = 2*(W + 8) + 2W

simplifying:

256 = 4W + 16, solve for W

pit the value of W back into the L equation to find L. These values should satisfy both formulas.