Constraints (Meta) Math Example 4

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Example 4

medium
A rectangle has area 36 cm² and integer side lengths. List all constraints and find all valid dimension pairs (l,w)(l, w) with l≥wl \ge w.

Solution

  1. 1
    Constraints: l⋅w=36l \cdot w = 36, both l,wl, w are positive integers, l≥wl \ge w.
  2. 2
    Factor pairs of 36 with l≥wl \ge w: (36,1),(18,2),(12,3),(9,4),(6,6)(36,1),(18,2),(12,3),(9,4),(6,6).

Answer

(36,1),(18,2),(12,3),(9,4),(6,6)(36,1),(18,2),(12,3),(9,4),(6,6)
Multiple constraints together (integer values, positive, product fixed, ordering) restrict the solution to a finite list. Systematically factoring under all constraints avoids missing solutions.

About Constraints (Meta)

Constraints are conditions, rules, or boundaries that restrict which values or solutions are allowed in a mathematical problem, narrowing an infinite space of possibilities to a manageable set.

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More Constraints (Meta) Examples

Example 1 easy

Solve [formula] and identify all constraints on [formula] before solving.

Example 2 medium

An integer [formula] satisfies two constraints: [formula] and [formula], and also [formula] is prime

Example 3 easy

State the domain constraint for [formula] and solve for [formula] when [formula].

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