Question

Gabe used 244 feet of fencing to enclose a rectangular garden and to put a divider between the two halves of the garden- the vegetable side and the herb side. The width of the garden is 32 feet less than its total length. Figure out the dimensions of the entire garden and then find the area of each half of the garden. Show all work

Answer 1

length = 68 feet

width = 36 feet

Area of each half of the garden = 1224 square feet

Explanation:

See attached figure at the bottom

Let the length of the garden be l and width be l-32

Since the garden is divided into two halves, the length would be split into two parts each of l/2

So,

AE =
`(l)/(2)`

EB =
`(l)/(2)`

AD = l-32

BC = l-32

DF=
`(l)/(2)`

FC =
`(l)/(2)`

EF = l-32

Total fence required = Sum of all sides + Middle side

244 = AE + EB + AD + BC + FC + DF + AD + EF

244 =
`(l)/(2)+(l)/(2)+l-32+l-32+(l)/(2)+(l)/(2)+l-32`

`3l+2l-(32+32+32)=244 = 244`

`5l-96=244`

Add 96 to both sides

`5l-96+96=244+96`

Cancel out -96 and +96 from the left side

`5l=340`

Divide both sides by 5

`(5l)/(5)=(340)/(5)`

Cancel out 5 from the top and bottom of the left side

l = 68

So, length = 68 feet

width = l-32

=>width = 68-32

=> width = 36 feet

Thus,
`AE = (l)/(2) = (68)/(2) = 34 feet`

EF = l-32 = 68-32 = 36 feet

Area of each half of the garden = AE * EF

=>Area of each half of the garden = 34 * 36

=> Area of each half of the garden = 1224 square feet