equation for perimeter is 2L +2W
perimeter of the lot is 390 ft
so we have 390 = 2L +2w
divide all terms by 2:
195 = L + W
rewrite this as L = 195-W ( eq.1)
cost of fence for the length = 36 per foot so we have 36L
cost of fence for width = 6 per foot so we have 6W
the fence was 1 length and 2 sides
so we have 36l + 6w +6w = total cost
total cost is 4980
so we have 4980 = 36L + 6w +6w
combine like terms:
4980 = 36L +12w
replace L with eq1 from above:
4980 = 36(195-w) +12w
distribute:
4980 = 7020 -36w +12w
combine like terms:
4980 = 7020-24w
subtract 7020 from both sides:
-2040 = -24w
divide both sides by -24:
-2040 / -24 = 85
width = 85 feet
using eq1 L = 195 - 85
Length = 110 feet
lond = 110 feet
short = 85 feet