Mr Chen used some identical rectangular tiles and black square tiles to decorate part of a floor as shown. The length of each tile is 43.5 cm.
- Find the width of each tile.
- Find the total area of the shaded regions.
Let the length of a rectangular tile be 1 L.
Let the width of a rectangular tile be 1 W.
5 L = 3 L + 3 W
5 L - 3 L = 3 W
2 L = 3 W
3 W = 2 x 43.5 = 87 cm
(a)
Width of one tile
= 87 ÷ 3
= 29 cm
(b)
Length of the square
= 1 L - 1 W
= 43.5 - 29
= 14.5 cm
Area of the square
= 14.5 x 14.5
= 210.25 cm
2 Area of the shaded regions
= 210.25 x 3
= 630.75 cm
2 Answer(s): (a) 29 cm; (b) 630.75 cm
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