Maria looks at the architectural plan of a four-walled room 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. (Short answer less than 200 words)
No, the room is not in the shape of a square.
In order to determine the shape of the room, we need to analyze the relationships between the different measurements given.
Since the walls meet each other at right angles, we can assume that the room is a rectangle, as squares are a special case of rectangles where all sides are equal in length.
Given that one wall in the plan has a length of 13 inches, we can infer that the adjacent wall is also 13 inches in length.
Next, we are provided with the measurement of the diagonal of the floor of the room in the plan, which is approximately 15.26 inches.
Using the properties of a rectangle, we can determine the relationship between the length and width of the room using the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the lengths of the other two sides.
Let's assume the width of the room is x inches. We can set up the following equation:
13^2 + x^2 = 15.26^2
Simplifying the equation:
169 + x^2 = 233.8276
Rearranging:
x^2 = 233.8276 - 169
x^2 = 64.8276
Taking the square root of both sides:
x ≈ √64.8276
x ≈ 8.05
Therefore, the width of the room is approximately 8.05 inches.
Since the length (13 inches) and the width (8.05 inches) are not equal, we can conclude that the room is not a square.