A scale drawing of a building in the shape of a pentagon has a perimeter of 75 inches. The scale of the actual building to the drawing is 307 feet to 5 inches. If each side of the building measures the same length, how long, in feet, is one side of the actual building?

The length of one side of the actual building is 921 feet

Step-by-step explanation:

If the scale of the actual building to the drawing is 307 feet to 5 inches, it means that 1 feet on the building would be

5/307 inches

The scale drawing of the building in the shape of a pentagon has a perimeter of 75 inches. A Pentagon has 5 sides. It means that the length of each side of the building on the drawing is

75/5 = 15 inches

Since 1 feet on the building = 5/307 inches on the drawing, then

x feet on the building = 15 inches on the drawing.

x = (15 × 307)/5 = 921 feet

921 feet

Step-by-step explanation:

If each side of the building measures the same length, and the perimeter is 75 inches, we have that each side in the scale drawing is 75/5 = 15 inches.

Now, to find the actual length of the building side, we can use a rule of three:

307 feet of actual side is 5 inches in the scale, so what's the length of the actual side for a 15 inches side in the scale:

307 feet -> 5 inches

x feet -> 15 inches

307/x = 5/15

5x = 307*15

x = 307*15/5 = 921 feet