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Figure This!


Complete Solution:

Each tile is 4 meters by 5 meters.

The area of each patio is 180 square meters (m2), and each is made from nine identical rectangular concrete pieces. This means that the area of one piece is 180 ÷ 9, or 20 m2.

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.

Alternate Solution:

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 W2 = 20
W2 = 4/5 × 20
W2 = 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.

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