Question

The perimeter of a rectangular lot of land is 392ft. This includes an easement of x feet of uniform width inside the lot on which no building can be done. If the buildable area is 136ft by 52ft, determine the width of the easement.

a) 50 ft
b) 60 ft
c) 70 ft
d) 80 ft

Answer 1

The question is about finding the easement width on a rectangular lot with a known perimeter. By using the perimeter formula for rectangles and knowing the builder area's dimensions, we can set up equations to solve for the easement width.

Step-by-step explanation:

The student is asking about the width of the easement on a rectangular lot of land with a perimeter of 392 feet. It is given that the build able area inside the lot has dimensions of 136 feet by 52 feet. To find the easement width, we must first determine the full dimensions of the lot including the easement on all sides.

The perimeter of a rectangle is calculated using the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. We know the perimeter (392 feet) and the dimensions of the build able area, so we can create two equations to solve for the length l and width w of the entire lot including the easement:

1) P = 2l + 2w where P is 392 feet.
2) The build able area is l - 2x by w - 2x where l and w include the easement and are therefore greater than 136 feet and 52 feet respectively.

First we can express the dimensions of the entire lot as l = 136 + 2x and w = 52 + 2x. Substituting these into the first equation we get:

392 = 2(136 + 2x) + 2(52 + 2x)

By solving this equation, we can find the value of x, the width of the easement.