A rectangular swimming pool has a diagonal that measures 19 yards and a side length that measures 15 yards. From this we can easily derive a right angled triangle with the hypotenuse (longest side) as 19 and one of the other sides as 15. The unknown side can be found using the Pythagoras' theorem as follows;
![\begin{gathered} AC^2=AB^2+BC^2 \\ AC=19 \\ BC=15 \\ AB=\text{???} \\ 19^2=AB^2+15^2 \\ 361=AB^2+225 \\ 136=AB^2 \\ \sqrt[]{136}=AB \\ AB=11.661903\ldots \\ AB\approx11.67 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/faoua6u61f66c7dniq9uzfsqgy5nivdz9x.png)
The width of the pool is approximately 11.67 yards.
The correct answer is option D