A rectangular savannah is 30m long by 15m wide. The Ministry of Education wants to fence that savannah using posts and wire. If the posts, costing $18.00 each, are placed 5m apart andt the wire cost $35.00 per metre. Calculate the cost of the posts and wire for fencing that savannah.
Along the length there will be 7 posts on each side. The width will only need one post each. 7x2 + 1x2 = 16 posts total
The length of the fence is the perimeter of the rectangle.
To calculate the cost of the posts and wire for fencing the rectangular savannah, we need to determine the perimeter of the savannah first.
The perimeter of a rectangle is given by the formula: P = 2 * (length + width)
For the given values, the length of the rectangular savannah is 30m and the width is 15m. Substituting these values into the formula, we get:
P = 2 * (30 + 15) = 2 * 45 = 90m
Therefore, the perimeter of the savannah is 90m.
Now, let's calculate the number of posts required. The posts are placed 5m apart, so we can divide the perimeter of the savannah by the distance between the posts:
Number of posts = Perimeter of savannah / Distance between posts
= 90m / 5m
= 18 posts
The cost of the posts is given as $18.00 each, so to find the total cost of the posts, we multiply the number of posts by the cost per post:
Cost of posts = Number of posts * Cost per post
= 18 posts * $18.00 per post
= $324.00
The cost of the wire is given as $35.00 per meter. To find the total cost of the wire, we need to multiply the perimeter of the savannah by the cost per meter:
Cost of wire = Perimeter of savannah * Cost per meter
= 90m * $35.00 per meter
= $3150.00
Finally, to calculate the total cost of the posts and wire for fencing the savannah, we add the cost of the posts and the cost of the wire:
Total cost = Cost of posts + Cost of wire
= $324.00 + $3150.00
= $3474.00
Therefore, the cost of the posts and wire for fencing the rectangular savannah is $3474.00.