Question P6 Repeated identity
Today’s problem — free all day, every step. Every day has one.
11 identical wooden planks are nailed together to build a large rectangular fence panel PQRS. 3 planks lie flat along the top and 8 planks stand upright below them, as shown. The perimeter of PQRS is 210 cm. Find the area of PQRS.
Answer
Each plank is 24 cm by 9 cm. PQ = 72 cm, PS = 33 cm, so the area of PQRS is 2376 cm².
One length or count, described two ways in the same question.
In this one. Repeated identity — one edge measured two ways gives one equation. PQ is 3 plank lengths and the very same PQ is 8 plank breadths, so 3L = 8B, and that alone fixes the shape of a plank.
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.
Worked examples of all 33 patterns and skills, in a booklet you can print.