To find the height of the pyramid, we can use the Pythagorean theorem. Let's label the right triangle formed by the height line, the slant height line, and the line segment connecting the center of the base to the center of the right base edge as triangle OHR.
Using the Pythagorean theorem, we have:
r² + h² = s²
Since we already know that s is 24 inches and e is 25 inches, we can find r.
r = √(e² - s²)
r = √(25² - 24²)
r = √(625 - 576)
r = √49
r = 7 inches
Now that we know r, we can substitute the values into the Pythagorean theorem to find h:
7² + h² = 24²
49 + h² = 576
h² = 576 - 49
h² = 527
h ≈ √527
h ≈ 22.92
Rounding to the nearest whole number, the height of the square pyramid is 23 inches.