Question

Matt 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 19 inches. The length of the diagonal of the floor of the room in the plan is approximately 20.62 inches.

Is the room in the shape of a square? Explain how you determined your answer. Show all your work.

Answer 1

no

Explanation:

if the room is a square, then all sides are equally long (19 in).

in any case, Pythagoras applies to calculate the length of the diagonal :

(side1)² + (side2)² = diagonal²

if both sides are equally long, that would mean

19² + 19² = 20.62²

361 + 361 = 425.1844

722 = 425.1844

that is not true, so the assumption that the room is a square is not true.