Maria looked at the architectural plan of a room with four walls in which the walls meet each other at right angles. The length of one wall in the plan is 13 inches. The length of the diagonal of the floor of the room in the plan is approximately 15.26 inches. Is the room in the shape of a square? Explain how you determined your answer. Show all your work.

Question

Carl Nolan

Mathematics

17 March, 01:18

Maria looked at the architectural plan of a room with four walls in which the walls meet each other at right angles. The length of one wall in the plan is 13 inches. The length of the diagonal of the floor of the room in the plan is approximately 15.26 inches. Is the room in the shape of a square? Explain how you determined your answer. Show all your work.

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Answers (1)

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Philip Archer · Answer 1

As all of the polygons that have four right angles are either rectangles or squares, you can create a right triangle using the length of the one wall and the diagonal, then use the Pythagorean Theorem to determine the length of the remaining side.

a²+b² = c²

13²+b² = 15.26²

169+b² = 232.8676

b² = 63.8676

b = 7.9917

Since a square has four equal sides, the length of a and b should be equal, but as they are not, that indicates that the room is a rectangle.