Examkin

Soru

Zorluk: OrtaPerimeter and Fencing Problems

A commercial facility is securing a right-triangular storage lot. The two perpendicular boundaries of the lot measure 6060 yards and 8080 yards. Security fencing will be installed along the entire perimeter to create a closed loop. If a support post must be placed every 1212 feet, how many total posts are required to complete the fence?

  1. A
    20
  2. B
    35
  3. 60Cevap
  4. D
    200

Cevap

60
The correct answer is found by first determining the hypotenuse of the right-triangular lot, which is 100 yards (602+802=100260^2 + 80^2 = 100^2). The total perimeter is 240 yards (60 + 80 + 100). Because the post spacing is given in feet, the perimeter must be converted to 720 feet (240 × 3). Finally, dividing the 720-foot boundary by the 12-foot spacing requirement yields exactly 60 posts.

Adım Adım Çözüm

1
Find the length of the third side of the lot using the Pythagorean theorem (a2+b2=c2a^2 + b^2 = c^2).
602+802=3600+6400=1000060^2 + 80^2 = 3600 + 6400 = 10000. The square root of 1000010000 is 100100 yards.
The boundary of a right-triangular lot includes the hypotenuse, which must be found to calculate the total perimeter.
2
Calculate the total perimeter of the triangular lot.
60+80+100=24060 + 80 + 100 = 240 yards.
The fencing will enclose the entire boundary of the lot.
3
Convert the perimeter into feet to match the unit of the post spacing.
240 yards×3 feet/yard=720 feet240 \text{ yards} \times 3 \text{ feet/yard} = 720 \text{ feet}.
Measurements must be in the same unit (feet) before dividing.
4
Divide the total perimeter by the distance required between each post.
720÷12=60720 \div 12 = 60 posts.
For a closed loop, the total number of posts equals the total perimeter divided by the spacing distance.

Anahtar Kavram

Calculating the perimeter of a right triangle using the Pythagorean theorem, converting units of measurement, and determining spacing requirements for closed boundaries.

Alternatif Yöntem

Instead of converting the perimeter to feet, convert the post spacing to yards. Since 3 feet equals 1 yard, 12 feet equals 4 yards. Divide the 240-yard perimeter by 4 yards to get 60 posts.
Tahmini Süre:1m 30s
Bu soruyu puanla

Konular

Perimeter and Fencing Problems

Bu konudan daha fazla soru