For the square pyramid, the lateral edge length, e , is 25 in., and the slant height, s , is 24 in. Find the height of the pyramid, h . Round the answer to the nearest whole number. Hint: Before finding the length of h , you will first need to find the length of r
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(1 point)
The height of the square pyramid is
in.
not 21
To find the height of the pyramid, we need to first find the length of the slant height \(r\).
In a square pyramid, the slant height (\(s\)) is the hypotenuse of a right triangle, with the height (\(h\)) as one of the legs and the lateral edge length (\(e\)) as the other leg.
Using the Pythagorean theorem, we can write the equation:
\[r^2 = h^2 + e^2\]
Substituting the given values, we have:
\[24^2 = h^2 + 25^2\]
Simplifying, we get:
\[576 = h^2 + 625\]
Rearranging the equation, we have:
\[h^2 = 576 - 625\]
\[h^2 = -49\]
Since the square of any real number cannot be negative, this equation has no real solutions. Therefore, the height of the square pyramid cannot be determined with the given information.