To prove that parallelogram PQRT is a rectangle, we need to show that it has right angles. One effective way to do this is by using the Pythagorean theorem.
Given the lengths \( l = 8 \) and \( w = 15 \), we can use the Pythagorean theorem in the context of a right triangle formed by the sides of the parallelogram. A parallelogram is a rectangle if its diagonals are equal or if the squares of its lengths and widths relate according to the Pythagorean theorem.
The statement that uses the Pythagorean theorem to relate the lengths and widths is:
\( 8^2 + 15^2 = TQ^2 \)
This expression indicates that if you consider a right triangle with legs of lengths 8 and 15, the square of the length of the diagonal (which is a side of the rectangle formed) would indeed relate to these two legs, confirming that there are right angles in the parallelogram, thus proving that it is a rectangle.
To summarize, the correct statement that proves parallelogram PQRT is a rectangle is:
\( 8^2 + 15^2 = TQ^2 \)