Perimeter problems

Many everyday problems turn out to be perimeter problems. Whenever something goes all the way round the edge (lace, tape, a fence, a rope, a running track), its length is the perimeter. A good habit: draw the shape first and write the lengths on it. Then you can see what goes round the edge.

Akshi wants to put lace all round a rectangular tablecloth 3 m long and 2 m wide. The lace needed is the perimeter: 2 × (3 + 2) = 2 × 5 = 10 m.

Usha takes three rounds of a square park of side 75 m. One round is the perimeter: 4 × 75 = 300 m. Three rounds is 3 × 300 = 900 m. In the same way, a farmer who puts 3 rounds of rope round a field 230 m long and 160 m broad needs 3 × perimeter. One round is 2 × (230 + 160) = 2 × 390 = 780 m, so the rope is 3 × 780 = 2340 m.

Money problems work the same way. To fence a park 150 m long and 120 m broad, the fence is 2 × (150 + 120) = 2 × 270 = 540 m long. At ₹40 per metre it costs 540 × 40 = ₹21,600.

Akshi runs 5 rounds of a rectangular track 70 m long and 40 m broad. Toshi runs 7 rounds of a smaller track, 60 m long and 30 m broad.

• One round for Akshi is 2 × (70 + 40) = 220 m, so she runs 5 × 220 = 1100 m.
• One round for Toshi is 2 × (60 + 30) = 180 m, so she runs 7 × 180 = 1260 m.

Toshi's track is smaller, but she runs more rounds, and she covers the longer distance.