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. (10 points)
To determine if the room is in the shape of a square, we need to compare the lengths of the walls.
Let's assume the length of the other wall is x inches.
Using the Pythagorean theorem, we can find the length of the diagonal of the floor:
diagonal = √(13^2 + x^2)
We are given that the diagonal is approximately 15.26 inches:
15.26 = √(13^2 + x^2)
Squaring both sides of the equation:
15.26^2 = 13^2 + x^2
233.8276 = 169 + x^2
x^2 = 233.8276 - 169
x^2 = 64.8276
Taking the square root:
x ≈ 8.05
The length of the other wall, x, is approximately 8.05 inches.
Since both walls are not equal, the room is not in the shape of a square.