Fencing the School Garden
A rectangular school garden is 18 metres long and 12 metres wide. The school wants to put a fence around the whole garden, leaving a 2-metre gap as a gate. Fence panels are sold in 3-metre lengths, and each panel costs 45 pula. The school also wants to plant a border of flowers along the inside edge of the garden, 1 metre wide, all the way round. The remaining inner rectangle will be planted with vegetables. The gardener says the flower border will need 4 times as much seed as a single 1-metre by 1-metre square would need, because there are four sides.
1. Calculate the total length of fencing needed (allowing for the gate) and the cost of the fence panels.
Read the worked answer
Perimeter of the rectangle = 2 × (18 + 12) = 2 × 30 = 60 metres.
Subtract the 2-metre gate: 60 − 2 = 58 metres of fencing needed.
Panels are 3 metres each. 58 ÷ 3 = 19 remainder 1. So 19 panels cover only 57 metres, which is not enough. The school must buy 20 panels (60 metres), with 2 metres spare.
Cost = 20 × 45 = 900 pula.
2. Find the area of the flower border and the area of the vegetable plot. Then judge whether the gardener's reasoning about the seed is correct.
Read the worked answer
Whole garden area = 18 × 12 = 216 square metres.
The border is 1 metre wide on every side, so the inner vegetable rectangle is (18 − 2) by (12 − 2) = 16 by 10 metres.
Vegetable area = 16 × 10 = 160 square metres.
Border area = 216 − 160 = 56 square metres.
The gardener said the border needs 4 times a 1 square metre unit, i.e. 4 square metres. That is wrong. The border is a frame, not four separate strips; its area is 56 square metres. The four strips overlap at the corners if counted as 18 + 18 + 12 + 12 = 60, and even that overcounts. The correct seed quantity is based on 56 square metres.