To find the height of the pyramid tent, we can use the relationship between the slant height, the height of the pyramid, and the half of the base edge length.
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First, let's find the half of the base edge length. Since the edge of the square base is 20 m, half of this length is: \[ \frac{20}{2} = 10 \text{ m} \]
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Now, we can apply the Pythagorean theorem. In a right triangle formed by the height of the pyramid (h), the half base edge (10 m), and the slant height (13.5 m), we have: \[ h^2 + 10^2 = 13.5^2 \]
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Calculate \(10^2\) and \(13.5^2\): \[ 10^2 = 100 \] \[ 13.5^2 = 182.25 \]
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Plug these values into the equation: \[ h^2 + 100 = 182.25 \]
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Solve for \(h^2\): \[ h^2 = 182.25 - 100 = 82.25 \]
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Now take the square root to find \(h\): \[ h = \sqrt{82.25} \approx 9.1 \text{ m} \]
Therefore, the height of the tent is approximately 9.1 m. The correct response is:
9.1 m