In the diagram, $\triangle P Q R$ has a right angle at $Q$. A square is drawn on each side of the triangle. The area of the square on side $Q R$ is 144 . The area of the square on side $P R$ is 169 . What is the area of the square on side $P Q$ ?
(A) 16
(B) 12
(C) 13
(D) 36
(E) 25

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-063.jpg?height=635&width=472&top_left_y=257&top_left_x=1293)
One way to phrase the Pythagorean Theorem is that the area of the square formed on the hypotenuse of a right-angled triangle equals the sum of the areas of the squares formed on the other two sides.

Therefore, the area of the square on $P Q$ equals the area of the square on $P R$ minus the area of the square on $Q R$, which equals $169-144$ or 25 .

ANSWER: (E)