Mathematical Modeling Math Example 3

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Example 3

easy
A rectangle has perimeter PP and length ll. Express the width ww as a function of PP and ll, then find ww when P=30P=30 and l=8l=8.

Solution

  1. 1
    Perimeter formula: P=2l+2wP = 2l + 2w. Solve for ww: w=P−2l2w = \dfrac{P - 2l}{2}.
  2. 2
    Substitute: w=30−162=142=7w = \dfrac{30 - 16}{2} = \dfrac{14}{2} = 7.

Answer

w=P−2l2,w=7w = \frac{P-2l}{2},\quad w = 7
Rearranging a known formula to express a different variable is basic mathematical modelling. The formula P=2l+2wP = 2l+2w models the perimeter, and algebra gives the width.

About Mathematical Modeling

The process of using mathematical structures — functions, equations, distributions — to represent, analyze, and predict real-world phenomena.

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