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Question 46

A room is a rectangle 10 metres by 6 metres, except that a rectangular corner piece 4 metres by 2 metres has been cut away, so the floor now has six straight edges. Select all the statements that are true about this room.

  1. Its perimeter is 32 metres, the same as the uncut rectangle.Correct answer
  2. Its perimeter is 26 metres, because the cut takes edge away.
  3. The two new edges together replace exactly the lengths they removed.Correct answer
  4. Cutting the corner away must shorten the perimeter, since the floor is smaller.

Explanation

Walking round the cut corner covers the same two distances that the cut took away, one across and one along, so the journey is still 10 plus 6 plus 10 plus 6. Expecting a shorter walk assumes that losing floor space must lose boundary too, yet the space inside and the distance round it can change quite independently.

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Question 46: A room is a rectangle 10 metres by 6 metres, except that a… · Geometry Basics · Questena