Answer:
(a) The possible dimensions are:
1 unit by 72 units; 2 units by 36 units; 3 units by 24 units; 4 units by 18 units; 6 units by 12 units; 8 units by 9 units
(b): Patio with greatest and the least perimeter
The dimension with the greatest perimeter is: 1 by 72
The dimension with the least perimeter is: 8 by 9
Step-by-step explanation:
Given
[tex]Tiles = 72[/tex]
Solving (a): Possible rectangular models
To do this, we simply list out the possible factor pairs of 72.
So, we have:
1 unit by 72 units; 2 units by 36 units; 3 units by 24 units; 4 units by 18 units; 6 units by 12 units; 8 units by 9 units
Solving (a): Models with the least and the greatest perimeter
Perimeter (P) is calculated using:
[tex]P = 2 * (L + W)[/tex]
So:
1 unit by 72 units;
[tex]P = 2 *(1 + 72) = 146 units[/tex]
2 units by 36 units;
[tex]P = 2 *(2 + 36) = 76 units[/tex]
3 units by 24 units;
[tex]P = 2 *(3 + 24) = 54 units[/tex]
4 units by 18 units;
[tex]P = 2 *(4 + 18) = 44 units[/tex]
6 units by 12 units;
[tex]P = 2 *(6 + 12) = 36 units[/tex]
8 units by 9 units
[tex]P = 2 *(8 + 9) = 34 units[/tex]
From the calculations above:
The dimension with the greatest perimeter is: 1 by 72
The dimension with the least perimeter is: 8 by 9
