Answer and your hired!Gardening Stinks:(

Question

An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 230 feet of antique picket fence are to be used to enclose the garden, find the dimensions of the garden.

 

The length is?

The width is?

Answer 1

The perimeter of the garden is

 

2 x width + 2 x length = perimeter.

 

If 230 ft of fence is used, then that means the perimeter equals 230.

 

We have that the width is

 

(2/3) x width = length

 

Let w be width and l be length.  We end up with two equations:

 

2w + 2l=230

2/3w=l

 

If we replace l in the first equation with its value from the second, we get an equation that has one variable, specifically w.

 

2w + 2l = 230

2w + 2(2/3)w = 230

(3/3)2w + 4/3w = 230

6/3w + 4/3w = 230

(6 + 4)/3w = 230

10/3w = 230

 

then w = 230(3/10) = 69.

 

Since we have w then we can solve for l.

 

2w + 2l = 230

2(69) + 2l = 230

2(69) - 2(69) + 2l = 230 - 2(69)

2l = 230 - 2(69)

2l = 92

l/2 = 92/2

l = 46