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.
(make it sound like an eight grade girl who wants to show her work but not a lot, also make it less than 200 words)
To determine if the room is in the shape of a square, I need to compare the lengths of the walls to see if they are equal. The length of one wall is given as 13 inches, but I don't have any information about the other walls.
However, I am given the length of the diagonal of the floor, which is approximately 15.26 inches. In a square, the diagonal of the floor is equal to the square root of 2 times the length of the wall.
Let's call the length of the other wall x. According to the Pythagorean theorem, the square of the diagonal (15.26^2) is equal to the sum of the squares of the two wall lengths (13^2 + x^2).
15.26^2 = 13^2 + x^2
233.0276 = 169 + x^2
x^2 = 233.0276 - 169
x^2 = 64.0276
x = sqrt(64.0276)
x ≈ 8
After calculating, I find that the length of the other wall is approximately 8 inches.
Since both walls have different lengths, the room is not in the shape of a square.