Final answer:
The dimensions of the base of the building are 300 feet by 125 feet.
Step-by-step explanation:
To find the dimensions of the base of the building, we can set up an equation based on the given information. Let's assume the width of the base is 'w' feet. According to the problem, the length of the base is 75 feet less than three times the width, which can be represented as 3w - 75.
The perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length, and w is the width. We are given that the perimeter of the base is 850 feet. Plugging in the length and width from above, we get:
850 = 2(3w - 75 + w)
Now we can simplify and solve for 'w':
850 = 2(4w - 75)
425 = 4w - 75
4w = 500
w = 125
Therefore, the width of the base is 125 feet. To find the length, we can plug in this value of 'w' in the expression 3w - 75:
length = 3(125) - 75 = 375 - 75 = 300 feet
So, the dimensions of the base are 300 feet by 125 feet.