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Question
Avneet buys 9 square paving slabs, each with a side of `1/2` m. He lays them in the form of a square.
- What is the perimeter of his arrangement [Fig (i)]?
- Shari does not like his arrangement. She gets him to lay them out like a cross. What is the perimeter of her arrangement [(Fig (ii)]?
- Which has greater perimeter?
- Avneet wonders if there is a way of getting an even greater perimeter. Can you find a way of doing this? (The paving slabs must meet along complete edges i.e. they cannot be broken.)
Solution
- Side of square = 3 × side
= `3 xx 1/2`
= `3/2`m
Perimeter of Square = `4 xx 3/2`
= 2 × 3
= 6 m - Perimeter = 0.5 + 1 + 1 + 0.5 + 1 + 1 + 0.5 + 1 + 1 + 0.5 + 1 + 1
= 10 m - The arrangement in the form of a cross has a greater perimeter.
- Perimeters greater than 10 m cannot be determined.
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