You desire to uncover the maximum area, so instead of the perimeter equation (eq1) into the area equation (eq2). This will gain the area equation in terms of just x.
You are watching: Find the length and width of a rectangle that has the given perimeter and a maximum area
Solve for x to get the critical value. This critical value is the size that will offer the maximum area. Then as soon as you have actually the length, plug it right into eq1 to get the width.
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