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Zorluk: OrtaPerimeter and Fencing Problems

A military engineering unit is installing a security fence around a rectangular vehicle depot. The depot is 150150 yards long and 8080 yards wide. The fencing plan includes leaving a single 3030-foot wide opening for a main access gate. If the fencing material costs $15\$15 per linear foot, what is the total cost of the fencing material needed? (Do not include commas or dollar signs in your answer)

Cevap: 20250 dollars

Cevap

20250
To find the total cost, first determine the total perimeter of the depot in yards: 2×(150+80)=4602 \times (150 + 80) = 460 yards. Since the fencing cost and gate width are in feet, convert the perimeter to feet: 460×3=1380460 \times 3 = 1380 feet. Next, subtract the 3030-foot gate opening where no fencing is needed: 1380−30=13501380 - 30 = 1350 feet of fencing. Finally, multiply the required fencing by the cost per foot: 1350×$15=$20,2501350 \times \$15 = \$20,250.

Adım Adım Çözüm

1
Calculate the perimeter of the rectangular depot in yards.
2(150+80)=2(230)=4602(150 + 80) = 2(230) = 460 yards.
The fencing will enclose the boundary of the rectangular area.
2
Convert the perimeter from yards to feet.
460×3=1380460 \times 3 = 1380 feet.
The cost of the fencing is given per linear foot and the gate is measured in feet, so all measurements must be in feet.
3
Subtract the gate opening from the total perimeter.
1380−30=13501380 - 30 = 1350 feet.
Fencing material is not needed for the gate opening.
4
Calculate the total cost of the fencing material.
1350×15=202501350 \times 15 = 20250 dollars.
The total length of fencing required is multiplied by the cost per linear foot.

Anahtar Kavram

Calculating perimeter, converting units (yards to feet), and determining total cost based on a linear rate.
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Konular

Perimeter and Fencing Problems

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