Question

Gina 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 17 inches. The length of the diagonal of the floor of the room in the plan is approximately 18.79 inches.
Is the room in the shape of a square? Explain how you determined your answer. Show all your work.

I would like to know what to do with the 18.79

Answer 1

If the shape of the room is a square, then the square root of the sum of the squares of the the two adjacent sides will give the diagonal.

i.e.

$\sqrt{17^2+17^2} = \sqrt{2(17^2)} \\ \\ = \sqrt{2(289)} = \sqrt{578} =24.04$

Since the square root of the sum of the squares of the the two adjacent sides is 24.04 and not 18.79, therefore, the shape of the room is not a square.