Solve the problem.
-Tom is going to build a fence around his garden which is a rectangle measuring $8 \mathrm{~m}$ by $16 \mathrm{~m}$. He will first put in posts which will be $4 \mathrm{~m}$ apart. If the posts cost $\$ 3.40$ each, what will be the total cost for all the posts?
A) $\$ 34.00$
B) $\$ 27.20$
C) $\$ 20.40$
D) $\$ 40.80$

Question

Quizplus · Accepted Answer

To find the total cost, first calculate the total number of posts needed. The perimeter of the garden is $2(8m + 16m) = 48m$. With posts $4m$ apart, including the corners, there are $12 + 4 = 16$ posts needed (each side has $4$ and $8$ posts respectively, but the corner posts are counted twice). At $\$3.40$ each, the total cost is $16 \times \$3.40 = \$54.40$. However, there seems to be a mistake in my calculation as none of the provided options match this result. Let's correct the calculation by accurately counting the posts: For each long side (16m), there are $16m / 4m = 4$ posts, plus one at each end, making it $5$ posts per long side. For the short sides (8m), there are $8m / 4m = 2$ posts, plus one at each end, making it $3$ posts per short side. However, the corner posts are counted for both adjacent sides, so we don't add extra for the corners. Thus, the total number of posts is $2(5 + 3) - 4 = 16 - 4 = 12$ (subtracting the 4 corner posts that were counted twice). The correct total cost is $12 \times \$3.40 = \$40.80$. My initial explanation contained a mistake in the calculation of the number of posts and their arrangement, leading to an incorrect total cost. The correct answer, considering the accurate count of posts needed for the perimeter with the given spacing and including the correction for the double-counted corner posts, aligns with option D.

Solve the Problem 8 m8 \mathrm{~m}8 m By 16 m16 \mathrm{~m}16 m He Will First Put in Posts Which Will Be

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