Lucinda wants to build a square sandbox, but she has no way of measuring angles. Explain how she can make sure that the sandbox is square by only measuring length. A. Arrange four equal-length sides so the diagonals bisect each other. B. Arrange four equal-length sides so the diagonals are equal lengths also. C. Make each diagonal the same length as four equal-length sides. D. Not possible; Lucinda has to be able to measure a right angle.
The Correct Answer and Explanation is:
Correct Answer: B. Arrange four equal-length sides so the diagonals are equal lengths also.
Explanation:
Lucinda wants to construct a square sandbox but does not have a tool to measure right angles. A square is a special type of rectangle where all sides are equal and all angles are right angles. Since Lucinda cannot check angles, she must rely only on lengths to confirm that the shape is a square.
First, she should make sure all four sides are equal. This alone will not guarantee a square, because a rhombus also has four equal sides but does not necessarily have right angles. A rhombus can look slanted, like a diamond.
To be sure the shape is a square and not a rhombus, Lucinda needs to check the diagonals. In a square, the diagonals are equal in length. In a rhombus that is not a square, the diagonals are not equal. So, if she constructs a four-sided figure with all sides equal and then measures both diagonals, she can be sure it is a square if both diagonals are also equal.
This method works because the only quadrilateral with all sides equal and both diagonals equal is a square. This gives Lucinda a reliable way to verify that her sandbox is square without needing to measure angles directly.
Option A, which states the diagonals bisect each other, applies to all parallelograms and not just squares. Option C is incorrect because in a square, the length of each diagonal is longer than a side and is not equal to the side. Option D is incorrect because measuring angles is not the only way to construct a square. Lucinda can use this length-based method to achieve her goal.
By following option B, she can be confident the sandbox is truly square.
