Final answer:
To find the dimensions of a rectangular piece of land, we can solve the problem using the given information and the formula for the perimeter of a rectangle. By setting up an equation and simplifying, we can find that the width is 70 units and the length is 315 units.
Step-by-step explanation:
To solve this problem, let's let the width of the rectangular piece of land be represented by w. Since the length is 35 units more than four times the width, we can represent the length as 4w+35.
To find the dimensions, we need to use the formula for the perimeter of a rectangle: P = 2L + 2W where P is the perimeter, L is the length, and W is the width. We know that the perimeter is 770, so we can set up the equation: 770 = 2(4w+35) + 2w.
Simplifying the equation, we get 770 = 8w + 70 + 2w. Combining like terms, we have 10w + 70 = 770. Subtract 70 from both sides to get 10w = 700, and then divide both sides by 10 to find w = 70.
So the width of the rectangle is 70 units. To find the length, we substitute this value of w back into the expression for the length: L = 4w + 35 = 4(70) + 35 = 315.
Therefore, the dimensions of the rectangular piece of land are width = 70 ft, length = 315 ft.