Playground Grass and Fence Budget
A school has a rectangular plot 60 m by 40 m for a playground. A basketball court 28 m by 15 m is to be placed inside the plot, leaving a 1.5 m wide walking path all around the boundary. The rest of the inner area will be grassed. Grassing costs ₹35 per square metre. Fencing costs ₹250 per metre and will run along three sides only; the fourth side, one 60 m side along the road, is an existing wall. A 3 m gate on one of the fenced sides will have no fence. The school has ₹80,000 for grass and fencing. The games teacher claims the grass area will give each of 200 cadets at least 8 square metres of play space.
1. Calculate the grass area and check the games teacher's claim for 200 cadets.
Read the worked answer
Outer plot area = 60 × 40 = 2,400 m². The path is 1.5 m wide inside the boundary, so the inner rectangle is (60 − 3) by (40 − 3) = 57 × 37 = 2,109 m². Path area = 2,400 − 2,109 = 291 m². Court area = 28 × 15 = 420 m². Grass area = 2,109 − 420 = 1,689 m².
Per cadet = 1,689 ÷ 200 = 8.445 m². This is at least 8 m², so the teacher's claim is true, but only just.
2. Calculate the total cost of grassing and fencing, and state whether it fits the ₹80,000 budget.
Read the worked answer
Grass cost = 1,689 × 35 = ₹59,115. Fencing: the wall is one 60 m side, so fence the other 60 m side and the two 40 m sides. Length = 60 + 40 + 40 = 140 m. Subtract the 3 m gate: 140 − 3 = 137 m. Fence cost = 137 × 250 = ₹34,250. Total = 59,115 + 34,250 = ₹93,365.
The budget is ₹80,000, so the plan is short by 93,365 − 80,000 = ₹13,365. The school cannot complete both works within the budget as stated.
3. If the path width is reduced to 1 m, does the school save enough to stay within ₹80,000? Explain carefully.
Read the worked answer
New inner rectangle = (60 − 2) by (40 − 2) = 58 × 38 = 2,204 m². Path area = 2,400 − 2,204 = 196 m², so less land is used by the path. Grass area = 2,204 − 420 = 1,784 m². Grass cost = 1,784 × 35 = ₹62,440. Fence cost is unchanged at ₹34,250. Total = ₹96,690.
This is higher than the 1.5 m plan, not lower. A narrower path leaves more grass, and grass is the larger cost. The saving would have to come from reducing the grassed area, the fence length, or the specification - not from shrinking the path.