Avneet buys $9$ square paving slabs, each with a side $\frac{1}{2} m$ . He lays them in the form of a square.

(a) What is the perimeter of his arrangement?

(b) Shari does not like his arrangement. She gets him to lay them out like a cross. What is the perimeter of her arrangement?

(c) Which has greater perimeter?

(d) 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.)

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Solution

(a) Perimeter of the square = $4 \times$ side.
Length of the side of the square $= 3$ square slabs $\times$ length of each side
$= 3 \times 0.5 m = 1.5 m [∵ each side = \frac{1}{2} m]$
Perimeter of Avneet's arrangement $= 4 \times 1.5 m = 6 m$

(b) Consider the figure

Perimeter of the figure $= 5 \times$ length of each side $= 5 \times 0.5 m = 2.5 m [∵ each side = \frac{1}{2} m]$

Perimeter of the cross $= 4 \times$ figure $= 4 \times 2.5 m = 10 m$

(c) Shari's arrangement (cross) has greater perimeter.

(d) No, but we can achieve the same perimeter as Shari's arrangement by arranging all the squares in a row.

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Avneet buys 9 square paving slabs, each with a side of m. He lays them in the form of a square.

(a) What is the perimeter of his arrangement [figure (i)]?

(b) Shari does not like his arrangement. She gets him to lay them out like a cross. What is the perimeter of her arrangement [figure (ii)]?

(d) 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.)

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