Find and interpret perimeter and circumference in numeric and contextual problems.
Find every matching boundary representation
Problem
Identify \(\text{every}~\text{card}\) with a perimeter or circumference of \(24~\text{units}\).
Cards: • A rectangle with side lengths \(8~\text{units}\) and \(4~\text{units}\) • A square with side length \(6~\text{units}\) • A triangle with side lengths \(7~\text{units}\), \(9~\text{units}\), and \(8~\text{units}\) • A circle with radius \(4~\text{units}\) • The expression \(2(5~+~7)\) • A garden where the distances around the \(\text{four}~\text{sides}\) are \(10~\text{ft}\), \(2~\text{ft}\), \(10~\text{ft}\), and \(2~\text{ft}\) • A regular pentagon with side length \(5~\text{units}\)
Big Picture
What this problem is really about
Treat the target boundary value as a test that every representation must pass independently. Add all outside sides for polygons and contextual figures, evaluate any given expression with its grouping intact, and use the circumference formula when a radius is supplied. Exact equality matters, so an approximation near the target does not count as a match.
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