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

The length of one wall of the room is 13 inches. If the room is squared shape, all the side lengths must be 13 inches.

Since the adjacent walls are at right angles to each other, the diagonal can be found using the Pythagorean Theorem. So if all side lengths are 13 inches each, the length of diagonal will be:

The length of this diagonal is different from the length of diagonal given. Hence this proves the shape of room is not square. Rather it is rectangular. 

We can find the exact length of other side by using the Pythagorean Theorem again. Let the length of other side is x, so

Therefore, length of the other side, rounded of to nearest inch is 8 inches.