A diagonal of a parallelogram measures 37 inches. The sides measure 35 inches and 1 foot. Is the parallelogram a rectangle?

No. A rectangle has 4 right angles. Thus, if this parallelogram was a rectangle, applying the Pythagorean theorem on its side lengths and diagonals must hold true.

35^2 + 1^2 ≠ 37^2

1225 + 1 ≠ 1369

1226 ≠ 1369

Thus the parallelogram is not a rectangle