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 34.5 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 34.5 = 69 cm
(a)
Width of one tile
= 69 ÷ 3
= 23 cm
(b)
Length of the square
= 1 L - 1 W
= 34.5 - 23
= 11.5 cm
Area of the square
= 11.5 x 11.5
= 132.25 cm
2 Area of the shaded regions
= 132.25 x 3
= 396.75 cm
2 Answer(s): (a) 23 cm; (b) 396.75 cm
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