a building in a city has a rectangular base. the lenght of the base measures 70 ft less than twice the width. the perimeter of this base is 820 ft.

P=2L+2W

820=2(2W-70)+2W
820=4W-140+2W
820=6W-140
820+140=6W
960=6W
160=W

To find the dimensions of the building's base, we can start by setting up two equations based on the given information:

Let the width of the base be represented by "w" in feet.
The length of the base is then 2w - 70 feet.

1) The perimeter of the base is the sum of all the sides, which is given as 820 feet:
Perimeter = 2(w + (2w - 70)) = 820

2) The length of a rectangle is the longer side, so in this case, it is 2w - 70 feet.

Now, let's solve these equations step-by-step:

1) Perimeter = 2(w + (2w - 70)) = 820
=> 2w + 2(2w - 70) = 820
=> 2w + 4w - 140 = 820
=> 6w - 140 = 820
=> 6w = 820 + 140
=> 6w = 960
=> w = 960/6
=> w = 160

2) Since the width is 160 feet, the length of the base is 2w - 70:
Length = 2(160) - 70 = 320 - 70 = 250

Therefore, the dimensions of the building's base are: Width = 160 feet and Length = 250 feet.

To find the dimensions of the rectangular base, we'll break down the problem step by step.

Let's assume the width of the rectangular base is 'W' ft.
According to the given information, the length of the base is "70 ft less than twice the width". Hence, the length, L, can be expressed as:
L = 2W - 70

The formula for the perimeter of a rectangle is given by:
Perimeter = 2(L + W)

We are given that the perimeter of the base is 820 ft, so we can substitute the values and solve for W.

820 = 2((2W - 70) + W)

Now, let's simplify the equation:

820 = 2(3W - 70)
Divide both sides by 2:
410 = 3W - 70
Add 70 to both sides:
480 = 3W
Divide both sides by 3:
W = 160

Therefore, the width of the rectangular base is 160 ft.
Now, substitute this value of W back into the equation for the length that we derived earlier:

L = 2W - 70
L = 2(160) - 70
L = 320 - 70
L = 250

Hence, the length of the rectangular base is 250 ft.

In summary, the width of the base is 160 ft, and the length is 250 ft.

P = 2L + 2W

820 = 2(W - 70) + 2W

820 = 4W - 140

820 - 140 = 4W

680/4 = W