Question

25 ft.
40 ft.

Apply the Pythagorean theorem to determine the height of the square pyramid, h. Round the answer to the nearest tenth.

47.2 ft.

15.0 ft.

32.0 ft

31.2 ft.

Answer 1

To determine the height of a square pyramid using the Pythagorean theorem, we use the relationship between the height \( h \), half the base length \( b/2 \), and the slant height \( s \).

Here, you provided dimensions that seem to relate to the square pyramid (base length and slant height). Let's assume:

- The base of the square pyramid is 40 ft (so half the base, \( b/2 = 20 \) ft).
- The slant height is 25 ft.

We apply the Pythagorean theorem:

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

Plugging in the values \( s = 25 \) ft and \( \frac{b}{2} = 20 \) ft:

\[
25^2 = h^2 + 20^2
\]

Calculating the squares:

\[
625 = h^2 + 400
\]

Now, isolate \( h^2 \):

\[
h^2 = 625 - 400
\]

\[
h^2 = 225
\]

Taking the square root of both sides, we find \( h \):

\[
h = \sqrt{225} = 15 \text{ ft}
\]

Thus, the height \( h \) of the square pyramid is:

\[
\boxed{15.0 \text{ ft}}
\]

This matches the answer you're looking for from the provided options.