Fencing the School Vegetable Plot
The Grade 5 class has a rectangular vegetable plot 10 m long and 6 m wide. They plan to fence it with wire mesh and wooden posts. Posts must be placed every 2 m along the boundary, including at every corner. There is a 2 m wide gate on one of the 10 m sides. The gate opening replaces one 2 m section of fence between two posts; the two posts on either side of the gate are still needed. Each post costs Rs. 250. Wire mesh costs Rs. 100 per metre. The class has Rs. 7,000 from a recycling project, but Rs. 500 must be kept for seeds. A shop gives 10% off posts if 15 or more are bought. The teacher asks the class to find out whether they can fence the whole plot now. They must also decide what to do if the money is not enough.
1. Calculate the length of wire mesh needed and its cost. Show each step.
Read the worked answer
Step 1 – Perimeter of the plot:
Perimeter = 2 × (length + width) = 2 × (10 + 6) = 32 m.
Step 2 – Subtract the gate:
The gate is 2 m wide and no wire is needed across it.
Wire needed = 32 − 2 = 30 m.
Step 3 – Cost of wire:
30 m × Rs. 100 per metre = Rs. 3,000.
Reasoning check: The wire does not go across the gate, but the posts at the gate sides are still part of the fence. So the wire length is 30 m, not 32 m. The class should record Rs. 3,000 for wire.
2. Calculate the number of posts needed, the post cost after discount, and the total cost. Compare this with the money available for fencing.
Read the worked answer
Step 1 – Count posts on the full boundary:
A closed rectangle with posts every 2 m has 32 ÷ 2 = 16 intervals and therefore 16 posts.
The gate replaces one 2 m interval, but the two posts on either side of the gate are still needed. So the class still needs 16 posts.
Step 2 – Post cost before discount:
16 × Rs. 250 = Rs. 4,000.
Step 3 – Discount:
16 posts is 15 or more, so the 10% discount applies.
10% of Rs. 4,000 = Rs. 400.
Post cost after discount = Rs. 4,000 − Rs. 400 = Rs. 3,600.
Step 4 – Total cost:
Wire Rs. 3,000 + posts Rs. 3,600 = Rs. 6,600.
Step 5 – Money available:
Rs. 7,000 − Rs. 500 for seeds = Rs. 6,500.
Conclusion: Rs. 6,600 is Rs. 100 more than Rs. 6,500. The class cannot fence the whole plot and still keep Rs. 500 for seeds. They are short by Rs. 100.
3. The class is short of money. Give one change that keeps the plan safe and fair, and explain its effect. Do not simply say 'raise more money'.
Read the worked answer
One practical change is to widen the gate from 2 m to 4 m, if the school agrees that a 4 m gate is safe.
Effect on wire: The gate now removes two 2 m intervals instead of one.
Wire = 32 − 4 = 28 m.
Wire cost = 28 × Rs. 100 = Rs. 2,800.
Effect on posts: The middle post between the two gate intervals is no longer needed.
Posts = 16 − 1 = 15.
Post cost before discount = 15 × Rs. 250 = Rs. 3,750.
Discount = 10% of Rs. 3,750 = Rs. 375.
Post cost after discount = Rs. 3,375.
New total: Rs. 2,800 + Rs. 3,375 = Rs. 6,175.
Money available after seeds is Rs. 6,500, so the class would have Rs. 325 left.
Judgement: This works only if a 4 m gate is safe and does not let animals into the plot. If not, the class should keep the 2 m gate and collect the extra Rs. 100 or ask the shop for a small discount on wire. The change must not make the fence unsafe just to save money.