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Find the Variables and Internal Dimensions For a Studio and Patio

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I am building a rectangular studio on south side of house, so that the north side of the studio will be a portion of the currrent south side of the house.

The studio walls are 2 feet thick, and the studio's inside south wall is twice as long as its inside west wall.

Also, I am building a semicircular patio around the studio, with sliding glass doors opening from the studio out onto the patio. The studio will be circumscribed by the semicircle. There is a large tree remaining for shade - it is 20 feet from the south side of the house.

What are variables, internal dimensions of rectangular studio if external area of studio will be 400 square feet.

How far will the semicircular patio extend past the house at the farthest point to the nearest tenth of foot.

Will be able to build patio without removing tree? Why? Why not?

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The Variables and Internal Dimensions For a Studio and Patio are found.