Question P6 Repeated identity
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7 identical rectangular photo frames are mounted together to form a large rectangular display board EFGH for a school exhibition. 2 frames lie flat along the top and 5 frames stand upright below them, as shown. The perimeter of EFGH is 204 cm. Find the area of EFGH.
Answer
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One length or count, described two ways in the same question.
In this one. Repeated identity: the width of the board is counted twice — as 2 lengths along the top and as 5 breadths along the bottom — and setting the two counts equal, 2L = 5B, fixes L : B = 5 : 2 without knowing either number.
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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