Example — understanding an algebra problem

Example — Understanding an algebra problem

“The perimeter of a rectangle is $24$ cm and its area is $32$ cm². How long are the sides?”

• Data: perimeter $2p = 24$, area $A = 32$.
• Unknowns: the lengths of the two sides. Let us call them $x$ (base) and $y$ (height).
• Useful diagram: a rectangle with base $x$ and height $y$; two equations — one for the perimeter, one for the area. Without yet doing anything, we have already turned the text into: $\begin{cases} 2x+2y = 24\\ x\cdot y = 32 \end{cases}$

Note: we have not yet solved anything. We have only rewritten the problem in mathematical language. This is the first move.

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Topics: Working method
Concepts: Data and unknowns · Problem solving
Skills: Modelling · Solving systems