Question

Keli and Mario are planning to plant rectangular gardens of the same length, side by side with fencing all around and dividing the two plots. The total amount of fencing is 100 feet. If the total area of the two plots is 336 square feet and the dimensions are integers, what is the length of the fence that divides the two plots?

Answer 1

Explanation:

Given

Total area of two plot
`A=336 ft^2`

Let l and b the length and width of plot

Perimeter for Fencing

`P=3l+4b`

`100=3l+4b-----1`

`A=336=2lb`

`lb=168 ft^2---2`

Put value of b in 1

`4* (168)/(l)+3l=100`

`672+3l^2=100 l`

`3l^2-100l+672=0`

`l=(100\pm √(100^2-4* 3* 672))/(2* 3)`

`l=(144)/(6),(56)/(6)`

so there can be two value of l i.e.
`24\ ft, 9.33\ ft`

for
`l=24\ ft,\ b=7\ ft`