A commercial facility is securing a right-triangular storage lot. The two perpendicular bo… — Armed Services Vocational Aptitude Battery (ASVAB)

A commercial facility is securing a right-triangular storage lot. The two perpendicular boundaries of the lot measure $60$ yards and $80$ yards. Security fencing will be installed along the entire perimeter to create a closed loop. If a support post must be placed every $12$ feet, how many total posts are required to complete the fence?

A
20
B
35
60Answer
D
200

Answer

The correct answer is found by first determining the hypotenuse of the right-triangular lot, which is 100 yards (

60^2 + 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.

Step-by-Step Solution

Find the length of the third side of the lot using the Pythagorean theorem (

a^2 + b^2 = c^2

60^2 + 80^2 = 3600 + 6400 = 10000

. The square root of

10000

100

yards.

The boundary of a right-triangular lot includes the hypotenuse, which must be found to calculate the total perimeter.

Calculate the total perimeter of the triangular lot.

60 + 80 + 100 = 240

yards.

The fencing will enclose the entire boundary of the lot.

Convert the perimeter into feet to match the unit of the post spacing.

240 \text{ yards} \times 3 \text{ feet/yard} = 720 \text{ feet}

Measurements must be in the same unit (feet) before dividing.

Divide the total perimeter by the distance required between each post.

720 \div 12 = 60

posts.

For a closed loop, the total number of posts equals the total perimeter divided by the spacing distance.

Key Concept

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

Alternative Method

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.

Estimated Time:1m 30s

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