A rectangular advertising banner must have an area of

MATHEMATICS · Multi-part · AoPS · Mathematics · One-Variable Linear Equations · One-Variable Linear Equations

Problem

A rectangular advertising banner must have an area of 18 m218\,\text{m}^2. Its width is fixed at 1.2 m1.2\,\text{m} to fit a roadside frame. (a) Let the required length of the banner be l ml\,\text{m}. Write a linear equation in one variable that represents the given information. (b) Solve the equation to determine the length ll. (c) A second banner of the same width is needed to cover 24 m224\,\text{m}^2. Without starting a new solution from the beginning, use the value of ll obtained in part (b) to find the corresponding length for the second banner and explain your reasoning. (d) Show that your result in part (c) is consistent with solving the equation 1.2l=241.2l = 24 directly.

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