To find the length of the edge of the square base of the pyramid, we can use the Pythagorean theorem. In a square pyramid, the height, half of the base edge, and the slant height form a right triangle.
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Let's denote:
- Height (h) = 321 ft
- Slant height (l_s) = 436.5 ft
- Half of the base edge (a) = x/2, where x is the length of the edge of the base.
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According to the Pythagorean theorem: \[ l_s^2 = h^2 + a^2 \]
Substituting the known values: \[ (436.5)^2 = (321)^2 + (x/2)^2 \]
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Calculate \( (436.5)^2 \) and \( (321)^2 \): \[ (436.5)^2 = 190,505.25 \] \[ (321)^2 = 103,041 \]
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Substitute these values back into the equation: \[ 190,505.25 = 103,041 + (x/2)^2 \]
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Rearranging gives: \[ (x/2)^2 = 190,505.25 - 103,041 \] \[ (x/2)^2 = 87,464.25 \]
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Taking the square root: \[ x/2 = \sqrt{87,464.25} \approx 295.7 \]
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Therefore, to find x: \[ x = 2 \times 295.7 \approx 591.4 \]
Thus, the length of the edge of the square base rounded to the nearest tenth is approximately 591.4 feet.