Question Repeated identity
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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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About this method
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.
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