Question

Look at the rectangle and the square:

12 in
6 in
Sam says: "The length of diagonal SQ is two times the length of diagonal OM."
Is Sam correct? Explain how you know with words and/or calculations.
This is an open-ended question, but sentence suggestions have been provided for you as a starting point.
Samis/is not correct because
(Explain your reasoning with words)
OR
My calculations show that Sam _is/is not correct. (Show your work)

Answer 1

Sam is not correct because the length of diagonal SQ is not two times the length of diagonal OM.

Step-by-step explanation:

Sam is not correct because the length of diagonal SQ is not two times the length of diagonal OM. The diagonal of a rectangle is longer than its sides while the diagonal of a square is equal to the side length multiplied by the square root of 2. In this case, the diagonal of the rectangle is √(12^2 + 6^2) = √(144 + 36) = √180 = 6√5, while the diagonal of the square is 12√2. Therefore, the diagonal of the rectangle is not two times the diagonal of the square.

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