To find the slant height of a square pyramid, we can use the Pythagorean theorem. The slant height (\(l\)) is the hypotenuse of a right triangle formed by half of the base side length (\(b\)) and the height (\(h\)) of the pyramid.
Given:
- Base side length, \(b = 12\) inches
- Height, \(h = 18\) inches
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First, find half of the base side length: \[ \frac{b}{2} = \frac{12}{2} = 6 \text{ inches} \]
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Now we can use the Pythagorean theorem: \[ l = \sqrt{h^2 + \left(\frac{b}{2}\right)^2} \]
Plugging in the values: \[ l = \sqrt{18^2 + 6^2} \] \[ = \sqrt{324 + 36} \] \[ = \sqrt{360} \] \[ \approx 18.97 \text{ inches} \]
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Rounding 18.97 to the nearest whole inch gives: \[ l \approx 19 \text{ inches} \]
Since 19 inches is not one of the provided responses, please verify that the base length and height values are correct (12 inches for the base length and 18 inches for height). If adjustments are necessary, let me know!