Final answer:
The dimensions of the rectangular lot are 162.67 feet by 325.34 feet. The perimeter equation is 2L + 2W = 74. The cost equation is L + 3.50W = 159.
Step-by-step explanation:
Let's say the length of the rectangular lot is L feet and the width is W feet.
The perimeter of a rectangle can be defined as: 2L + 2W.
According to the question, the perimeter is 74 feet, so we can write the equation as: 2L + 2W = 74.
The cost of fencing along the two lengths is $1 per foot, so the cost for the length fencing is 1 * L dollars.
The cost of fencing along the two widths is $3.50 per foot, so the cost for the width fencing is 3.50 * W dollars.
The total cost of fencing is $159, so we can write the equation as: 1 * L + 3.50 * W = 159.
Now we have two equations:
2L + 2W = 74
L + 3.50W = 159
To solve these equations, we can use substitution or elimination method.
Let's use the elimination method:
- Multiply the second equation by 2 to eliminate L: 2L + 3.50W = 318
- Subtract the first equation from the second: (2L + 3.50W) - (2L + 2W) = 318 - 74
This simplifies to: 1.50W = 244.
Divide both sides by 1.50: W = 244 / 1.50 = 162.67 feet.
Plug this value back into the first equation to find L: 2L + 2(162.67) = 74.
Simplify: 2L + 325.34 = 74.
Subtract 325.34 from both sides: 2L = -251.34.
Divide both sides by 2: L = -251.34 / 2 = -125.67 feet.
Since the dimensions of the lot cannot be negative, we discard the negative value.
Therefore, the dimensions of the lot are 162.67 feet by 325.34 feet.