Question

Find the slant height of the square pyramid base side length 16 and altitude is 15

Answer 1

To find the slant height of a square pyramid, we can use the Pythagorean theorem. The slant height (\( l \)) is the hypotenuse of a right triangle formed by the altitude of the pyramid (\( h \)), half of the base length (\( \frac{s}{2} \)), and the slant height itself.

### Given:
- Side length of the base (\( s \)) = 16
- Altitude (\( h \)) = 15

### Steps:

1. **Find half of the base length:**
\[
\frac{s}{2} = \frac{16}{2} = 8
\]

2. **Use the Pythagorean theorem:**
The right triangle is formed by the altitude, half of the base length, and the slant height. Therefore:
\[
l^2 = h^2 + \left(\frac{s}{2}\right)^2
\]
Substituting the known values:
\[
l^2 = 15^2 + 8^2
\]
\[
l^2 = 225 + 64
\]
\[
l^2 = 289
\]

3. **Solve for \( l \):**
\[
l = \sqrt{289} = 17
\]

### Conclusion:
The slant height of the square pyramid is \( \boxed{17} \).