A field is a rectangle with a perimeter of 1040 feet. The length is 300 feet more than the width. Find the width and the length of the rectangular field. What is the width of the rectangular field?

Accepted Solution

Answer:Width = 110 ftStep-by-step explanation:width = xlength = x + 300To find the width, we use the formula for perimeter, substituting 1040 for perimeter, x + 300 for length, and x for width:[tex]P=2(l+w)\\\\1040=2[(x+300)+x][/tex]Combine like terms inside the brackets:[tex]1040=2(2x+300)[/tex]Distribute the 2 within the parentheses:[tex]1040=4x+600[/tex]Subtract 600 from both sides:[tex]440=4x[/tex]Divide both sides by 4:[tex]110=x[/tex]Therefore, the width is 110 ft and the length is 410 ft. To verify, we can check that the perimeter equals 1,040 ft.[tex]P=2(l+w)\\P=2(410+110)\\P=2(520)\\P=1040\\Check.[/tex]