Question

Avneet buys 9 square paving slabs, each with a side of $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ m. He lays them in the form of a square.


(i) What is the perimeter of his arrangement?
(ii) Shari does not like his arrangement. She gets him to lay them out like a cross. What is the perimeter of her arrangement?
(iii) Which has greater perimeter?
(iv) 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 they cannot be broken)

Answer 1

(i) Length of the side of one slab = 1/2 m
In the square arrangement, one side of the square is formed by three slabs.
So, length of the side of the square = 3 $\times \frac{1}{2}$= 3/2 m
The perimeter of the square arrangement = 4 $\times \frac{3}{2}$ = 6 m
(ii) The cross arrangement consists of 8 sides. These sides form the periphery of the arrangement and measure 1 m each.
Also, this arrangement consists of other 4 sides that measure 1/2 m each.
So, the perimeter of the cross arrangement = (1 + 1/2 + 1 + 1 + 1/2 + 1 + 1 + 1/2 + 1 + 1 + 1/2 + 1)
= (8 + 2) = 10 m











(iii) Perimeter of the cross arrangement = 10 m
Perimeter of the square arrangement = 6 m
Thus, the perimeter of the the cross arrangement is more than that of the square arrangement.

(iv) No, there is no way of arranging these slabs where the perimeter is more than 10 m.