Question

The pyramids length is 13
The pyramids base is 16 each line
What is the slant height of this square pyramid
14, 8, 289, 17

Answer 1

To find the slant height of a square pyramid, you can use the Pythagorean theorem. The slant height \( l \) is related to the height \( h \) and half of the base length \( b \).

Given:
- The length of the pyramid \( h = 13 \) (this is the vertical height)
- The base length \( b = 16 \)

First, we find half of the base length:

\[
\frac{b}{2} = \frac{16}{2} = 8
\]

Now, we can apply the Pythagorean theorem:

\[
l = \sqrt{h^2 + \left(\frac{b}{2}\right)^2}
\]

Substituting the known values:

\[
l = \sqrt{13^2 + 8^2}
\]
\[
l = \sqrt{169 + 64}
\]
\[
l = \sqrt{233}
\]

Thus, the slant height is:

\[
l \approx 15.23
\]

Since 15.23 is not one of the options given (14, 8, 289, 17), we conclude that none of those values represent the slant height based on the calculations.

If you require a specific reasonable approximation based on those options, the closest whole number would be **17**, although it's not the exact calculation.