Question

a construction company has adjoined a 4400 ft2 rectangular enclosure to its office building. three sides of the enclosure are fenced in. the side of the building adjacent to the enclosure is 440 ft long and a portion of this side is used as the fourth side of the enclosure. let x and y be the dimensions of the enclosure, where x is measured parallel to the building, and let l be the length of fencing required for those dimensions. (a) find a formula for l in terms of x and y .

Answer 1

The required formula is l=900.

Since the side of the building adjacent to the enclosure is 440 ft long and it is one of the dimensions of the enclosure, the other dimension is x feet. Hence, the area of the rectangular enclosure is 440x square feet.

Since this area is also 4400 square feet, we have

440x &= 4400

x &= 10

Thus, the dimensions of the rectangular enclosure are 10 feet by 440 feet. Therefore, the length of the fencing required for these dimensions is

l &= 10 + 440 + 10 + 440 \

&= 900

Therefore, the required formula is l=900.