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Zorluk: OrtaPerimeter and Fencing Problems

An airport authority is installing a security barrier around a new rectangular radar facility. The facility measures 4040 yards in length and 3232 yards in width. The design for the security barrier requires a heavy-duty steel post at each of the four corners, with additional posts placed exactly every 88 feet along all four sides. How many steel posts are required in total to enclose the facility?

Cevap: 54 posts

Cevap

54 posts are required in total.
The correct answer is found by first ensuring all units match. Converting the dimensions to feet gives a length of 120 feet and a width of 96 feet. The total perimeter is 432 feet. Dividing this continuous perimeter by the 8-foot spacing requirement yields exactly 54 posts.

Adım Adım Çözüm

1
Convert the given dimensions from yards to feet.
Length = 40 * 3 = 120 feet. Width = 32 * 3 = 96 feet.
The post spacing is provided in feet, so all measurements must be converted to the same unit before calculating the perimeter.
2
Calculate the total perimeter of the rectangular facility.
Perimeter = 2 * (120 + 96) = 2 * 216 = 432 feet.
The security barrier encloses the entire outer boundary of the facility, which corresponds to its perimeter.
3
Determine the total number of posts required.
Total posts = 432 / 8 = 54.
For any closed loop, the total number of equally spaced posts equals the total perimeter divided by the distance between the posts.

Anahtar Kavram

Calculating perimeter of a rectangle, unit conversions, and dividing a perimeter into equal segments.
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Perimeter and Fencing Problems

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