Martin has 120 feet of fencing to enclose two rectangular play areas for children. He plans to enclose a rectangular area and then divide it into two sections. Find the dimensions of the largest total area Martin can enclose.

Question

Martin has 120 feet of fencing to enclose two rectangular play areas for children.  He plans to enclose a rectangular area and then divide it into two sections.   Find the dimensions of the largest total area Martin can enclose.

Alexis1415 · Answer

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Vocaloid · Answer

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because there's two sections in this rectangle, we have 3 sections for the width, and 2 for the length

total perimeter = 3W + 2L = 120 feet

solve this equation for either W or L (it doesn't matter in the end). plug that equation into the area equation (Area of the whole rectangle = L*W) to reduce this equation to one variable. graph the function, find the maximum area.