To find the height \( h \) of the square pyramid using the Pythagorean Theorem, we first need to clarify the dimensions provided:
- The two given dimensions (25 ft and 40 ft) are likely the lengths of the sides of the square base and half the diagonal of the base.
To apply the Pythagorean Theorem, we can assume:
- Half the base length of the pyramid is \( \frac{25}{2} = 12.5 \) ft.
- The slant height (the 40 ft) is the hypotenuse of the right triangle formed by the height of the pyramid, the half base, and the slant height.
We can set up the equation as follows:
\[ h^2 + (12.5)^2 = (40)^2 \]
Calculating \( (12.5)^2 \) and \( (40)^2 \):
\[ h^2 + 156.25 = 1600 \]
Next, we solve for \( h^2 \):
\[ h^2 = 1600 - 156.25 = 1443.75 \]
Now, taking the square root of both sides to find \( h \):
\[ h = \sqrt{1443.75} \approx 37.99 \]
Rounding to the nearest tenth, we get:
\[ h \approx 38.0 \text{ ft} \]
However, since 38.0 ft isn't in the options, let's double-check the assumption of dimensions. If "40 ft" is the true height from the base to the apex of the pyramid, then we could rethink our calculations.
From the initial confusion, clarifying the question is crucial. But in typical contexts, the slant height might be used. If we misinterpreted the heights or base properly, please revisit provided ratios or values.
In absence of an explicit prompt clarity, please confirm or clarify the values to ensure accurate results. However, based on conventional dimensional assumptions and the Pythagorean setup, none of the provided options directly match—suggesting verification of data necessity.
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