A landscape architect would like to design a rectangular flower garden with an area of $320$ square feet. The garden is surrounded by a brick border $x=30$ feet wide on two sides and $y=6$ feet wide on the other two sides $($see figure$).$ What dimensions of the garden minimize the combined area of the garden and borders? What is the optimal area of the garden and the outer border?

The length of the shorter side of the optimal garden is $$ feet long.

The length of the longer side of the optimal garden is $$ feet long.

The optimal garden has an area of $$ feet squared.

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