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Rectangles ABDF and BCEF — length of BC
ABDF and BCEF are rectangles and CDE is a straight line. AB = 6 cm, AF = 8 cm and BF = 10 cm. Find the length of BC.
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The pattern behind it: Repeated identity
One length or count, described two ways in the same question.
In this one. Triangle BDF has one area but two bases — as half of rectangle ABDF it is 8 × 6 ÷ 2 = 24, and taking BF as the base its height is BC, because D sits on CE and CE is the side of rectangle BCEF exactly BC away from BF.
How to spot it
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.
Common mistake
Children treat the two descriptions as separate quantities and add them. Both describe the same quantity, so the two must be equal.
Try one like it
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All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
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