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 eights grader response)
No, the room is not in the shape of a square.
To determine this, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, one of the walls is the hypotenuse of a right triangle, and the given diagonal of the floor is also the hypotenuse of a right triangle. We can use the Pythagorean theorem to compare the lengths of the walls to the length of the diagonal.
Let's call the length of the other wall x. Now the length of the diagonal of the floor (15.26 inches) is equal to the hypotenuse of a right triangle with one leg measuring 13 inches (one of the walls) and the other leg measuring x inches (the other wall).
Applying the Pythagorean theorem, we get:
(13)^2 + (x)^2 = (15.26)^2
169 + x^2 = 233.5876
x^2 = 233.5876 - 169
x^2 = 64.5876
x ≈ √64.5876 ≈ 8.04 inches
Since the length of the other wall is approximately 8.04 inches, we can conclude that the room is not a square because the lengths of the two walls are different. A square has four equal sides, and in this case, the lengths of the walls are not equal.