Question P6 Repeated identity
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9 identical rectangular tiles are used to make a mosaic panel WXYZ for a bathroom wall. 4 tiles are laid flat along the top and 5 tiles are stood upright below them, as shown. The perimeter of WXYZ is 174 cm. Find the area of WXYZ.
Answer
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One length or count, described two ways in the same question.
In this one. The edge WX is the same length read two ways — as 4 tile-lengths and as 5 tile-breadths — so 4L = 5B, and that one equation fixes the ratio L : B = 5 : 4 before any number is used.
A shape or count is described from two viewpoints in the same question, such as one edge measured as a number of long pieces and again as a number of short pieces.
Children treat the two descriptions as separate quantities and add them. Both describe the same quantity, so the two must be equal.
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