Each
tile is 4 meters by 5 meters. |
The area of each patio is 180 square
meters (m^{2}), and each is made from nine identical
rectangular concrete pieces. This means that the area
of one piece is 180 ÷ 9, or 20 m^{2}.
Since the area of the rectangle equals length (L) times
width (W), you know that L ×
W = 20. From the way in which the pieces are arranged
in Polygon’s patio, you can see that four lengths
is the same as five widths. In other words, the ratio
of length to width is 5 to 4.
As it happens, 5 ×
4 = 20. This means that the length is 5m, while the width
is 4m. |

Another way to look at this is as follows.
You know from Polygon’s patio that four lengths equals
five widths. Since 4L = 5W, then:
L = 5/4 ×
W
You also know the area of the piece:
L ×
W = 20. So, substituting for L,
(5/4 ×
W) ×
W = 20
5/4 W^{2} = 20
W^{2} = 4/5 ×
20
W^{2} = 16
W = 4 (Widths cannot be negative.)
Substituting 4 for W, you can then determine that L =
5. So a single concrete piece has dimensions 4m by 5m. |