To find the slant height of a pyramid, we can use the Pythagorean theorem. In a pyramid, the slant height is the hypotenuse of a right triangle formed by the height of the pyramid and half of the base.
Here, the height \( h \) is 15 and the base \( b \) is 16, so half of the base (\( \frac{b}{2} \)) is:
\[ \frac{16}{2} = 8 \]
Now, applying the Pythagorean theorem:
\[ \text{slant height} (l) = \sqrt{(\text{height})^2 + (\frac{b}{2})^2} \]
Substituting the values:
\[ l = \sqrt{15^2 + 8^2} \] \[ l = \sqrt{225 + 64} \] \[ l = \sqrt{289} \] \[ l = 17 \]
So the slant height of the pyramid is 17.
The correct response is 17.