To solve for the height of the square pyramid, we can use the Pythagorean theorem. The base of the pyramid forms a right triangle with the height of the pyramid and the line from the apex of the pyramid to the midpoint of one of the sides of the base.
Given:
- The right base side length (one side of the square pyramid) is 25 ft.
- The length of the bottom line (the diagonal across the rectangular base) is 40 ft.
Let's denote:
- The height of the pyramid as \( h \).
- Half of one side of the base pyramid as \( \frac{25}{2} = 12.5 \) ft.
- The diagonal across the base can be found with the Pythagorean theorem.
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Find the hypotenuse using the base's half side and height:
According to the Pythagorean theorem in one triangle with height and half the side of the base: \[ h^2 + (12.5)^2 = (20)^2 \]
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Substituting known values:
\[ h^2 + 12.5^2 = 20^2 \] Calculating \( 20^2 = 400 \) and \( 12.5^2 = 156.25 \): \[ h^2 + 156.25 = 400 \]
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Solving for \( h^2 \):
\[ h^2 = 400 - 156.25 \] \[ h^2 = 243.75 \]
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Finding \( h \):
\[ h = \sqrt{243.75} \approx 15.6 \]
After rounding the answer to the nearest tenth, the height \( h \) of the square pyramid is 15.6 ft.
None of the options provided (150円, 3208, 03128, 47.28) match the calculated height of approximately 15.6 ft. It seems there may have been a misunderstanding regarding the dimensions or requirements of the problem. Please double-check the details or clarify further if needed.
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