Final answer:
By setting up equations based on the perimeter formula and the given relationship between the length and width, we deduce that the actual dimensions of the building are 315 ft in length and 130 ft in width.
Step-by-step explanation:
To determine the dimensions of the base of the building with a rectangular shape, we first need to set up equations based on the information provided. The length (L) is described as 75 feet less than 3 times the width (W), and thus we can express this relationship as L = 3W - 75.
The perimeter (P) of a rectangle is given by the formula P = 2L + 2W, which in this case is 890 feet. By substituting the expression for L into the perimeter equation, we get 890 = 2(3W - 75) + 2W, or 890 = 6W - 150 + 2W, which simplifies to 8W = 1040. Dividing both sides of the equation by 8 yields W = 130 feet.
Now that we have the width, we can find the length by substituting W back into the length equation: L = 3(130) - 75 = 390 - 75 = 315 feet. Therefore, the actual dimensions of the building are 315 ft by 130 feet.