Question

A pool is surrounded by paving blocks which are 1 metre square. There are 16 blocks are used to surround the pool.

a) What is the perimeter of the pool?
b) What are the area of the various pools which could be surrounded by these 16 blocks?

Answer 1

have you drawn a diagram on graph paper?

or maybe actually used some tile, such as Scrabble pieces?
Consider a square, 3x3 surrounded by tiles. Are there 16 tiles?

Answer 2

yes I have the diagram in my hw book

I'm just not sure how to find the perimeter and area

the diagram has 4 blocks on each side... so 4 blocks on the top, 4 blocks on both sides, and 4 blocks on the bottom

Answer 3

well, geez - count the area! The blocks each take up 1m of width, so if the square's outside is 4x4, the inside is 3x3 making an area of 9

If the outside dimensions are x,y then the perimeter is 2(x+y)
We need 2(x+y)=16, so x+y=8
You can see that the inner dimensions are (x-1),(y-1), so the inner perimeter is 2(x+y-2) = 2(6) = 12 and the area is (x-1)(y-1)

So, what other combinations of x,y add up to 8?
Note that the smallest of the pair must be at least 2, since otherwise you just have a line of blocks, not a rectangle enclosing some hopefully nonzero area.

Answer 4

[AI-generated answer — Explain Bot]

To find the perimeter of the pool, we need to calculate the distance around the pool.

a) Perimeter of the pool:
Since each block is 1 meter square, the length of each side of a block is 1 meter.
There are 16 blocks used to surround the pool.

Let's assume the pool is rectangular in shape.
The number of blocks used along the length of the pool (L) is 2, as there are blocks on both sides.
The number of blocks used along the width of the pool (W) is 2, as there are blocks on both ends.
Therefore, the perimeter of the pool is calculated as:
Perimeter = 2L + 2W
= 2(2) + 2(2)
= 4 + 4
= 8 meters

b) Area of the various pools surrounded by 16 blocks:
Since we have 16 blocks available, let's calculate the different pool areas possible using those blocks.

To maximize the area, we need to arrange the blocks in a square shape.
The maximum number of full blocks that can be used to form a square is the square root of 16.
√16 = 4
So, we can arrange the blocks in a 4x4 square, as shown below:

[ X X X X ]
[ X X X X ]
[ X X X X ]
[ X X X X ]

In this case, all 16 blocks are used to form the pool area. Each block has an area of 1 square meter.
Therefore, the area of this pool is:
Area = Length × Width
= 4 meters × 4 meters
= 16 square meters

So, the various pools that can be surrounded by these 16 blocks would have an area of 16 square meters.