Arectangle pqrs and square lmno are drawn side by side. the length sr of the rectangle is labeled as 14 inches, and the width qr is labeled as 7 inches. the side lm of the square is labeled as 7 inches.

anna says that the length of diagonal sq is two times the length of diagonal om.

is anna correct? justify your answer and show all your work. your work should state the theorem you used to find the lengths of the diagonals.

Okay, so the square all sides are 7 so the diagonal using the 45-45-90 triangle theorem you can find that the diagonal is 7 times the square root of 2.  The diagonal of the rectangle can be found because it will divide the rectangle into 2 30-60-90 triangles.  The hypotenuse is 2 times the smallest side in a 30-60-90.  We know that the smallest side is 7.  So the hypotenuse is 14 (I think there is an error in the question).  We know this using the 30°-60°-90° Triangle Theorem.  Because 14 is not 2 times 7 times the square root of 2.  Anna is incorrect.  I think.

Sis less than or equal to 75 (bottom left)