Afarmer wanted to fence his private garden to keep out wandering cattle. the garden measured 26m by 40m. the fence had 5 strands of wire, and posts were placed every 2 metres. a) calculate the perimeter. b) what length of wire was needed? c) how many post were needed? d) find the total cost of the fence if witw was $0.28 per metre and each post cost $3.95.

The garden is in a rectangular shape with dimensions of 26m x 40m.

Number of wires in the fence = 5 strands

Distance between two posts = 2 metres

Part A

Perimeter of the garden = 2 × (l + b)

We know l = 40 m and b = 26 m

Substituting the values in the perimeter formula

⇒ Perimeter = 2 × (40 + 26)

⇒ Perimeter = 2 × 66

⇒ Perimeter = 132 meters

Part B

Length of wire needed = Strands of wire in the fence × Perimeter

⇒ Length of wire needed = 5 × 132

⇒ Length of wire needed = 660 meters

Part C

Number of Posts Needed = Perimeter ÷ Distance between two posts

⇒ Number of Posts Needed = 132 ÷ 2

⇒ Number of Posts Needed = 66

Part D

Total Cost of Fencing = ?

Per metre cost of wire = $0.28

Cost of each post = $3.95

⇒ Total Cost of Fencing = (Per metre cost of wire × Length of wire needed) + (cost of each post x Number of posts needed)

⇒ Total Cost of Fencing = (0.28 × 660) + (3.95 × 66)

⇒ Total Cost of Fencing = (184.8) + (260.7)

⇒ Total Cost of Fencing = $445.5

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