To find the length of the base of the square pyramid, we can use the properties of a right triangle formed by the height of the pyramid, half of the base length, and the slant height.
Let's denote:
- The height of the pyramid (h) = 20 miles
- The slant height (l) = 25 miles
- Half of the base length (b/2)
According to the Pythagorean theorem, we can set up the following equation:
\[ (h)^2 + (b/2)^2 = (l)^2 \]
Substituting in the known values:
\[ (20)^2 + (b/2)^2 = (25)^2 \]
Calculating the squares:
\[ 400 + (b/2)^2 = 625 \]
Now, to isolate the term with \(b\):
\[ (b/2)^2 = 625 - 400 \] \[ (b/2)^2 = 225 \]
Now take the square root of both sides:
\[ b/2 = \sqrt{225} = 15 \]
To find the full base length \(b\), we multiply by 2:
\[ b = 2 \times 15 = 30 \text{ miles} \]
Thus, the length of the base of the square pyramid is 30 miles.
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