You are working on plans for an elevator for an amusement ride. a square-shaped car measuring 3 m * 3 m will enter the elevator, which will spin it around 180 degrees while carring it to the next floor. This means the car will enter the elevator in one direction, rotate. and then exit the elevator through the same door but facing the opposite direction. Calculate the minimum dimension for the elevator that will allow the to turn. Allow 50cm on each side : What would the longest dimension of the car be?)

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You are working on plans for an elevator for an amusement ride. a square-shaped car measuring 3 m * 3 m will enter the elevator, which will spin it around 180 degrees while carring it to the next floor. This means the car will enter the elevator in one direction, rotate. and then exit the elevator through the same door but facing the opposite direction. Calculate the minimum dimension for the elevator that will allow the to turn. Allow 50cm on each side : What would the longest dimension of the car be?)

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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so the square-shaped car needs the least area to turn if it rotates round its center. try to imagine the picture in your mind, and you will see that the area required is a circle with the radius of 3sqrt(2)/2. so the minimum dimension of the elevator should be 3sqrt(2) m * 3sqrt(2) m.
when it is required to allow 50cm on each side, then the dimension of the elevator would be (3sqrt(2)+1) m * (3sqrt(2)+1) m . set the longest dimension of the car as x m*x m. then xsqrt(2)=3sqrt(2)+1, x=3+sqrt(2)/2. so the longest dimension of the car is (3+sqrt(2)/2) m by (3+sqrt(2)/2) m.

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