Final answer:
To find the height of the square pyramid, first calculate the half-diagonal of the base using the Pythagorean theorem with edge length and slant height. Then, apply the theorem again to solve for the height, rounding the result to the nearest whole number.
Step-by-step explanation:
To find the height, h, of the square pyramid when given the lateral edge length, e, and the slant height, s, we must first find the length of the base half-diagonal, r. Since the lateral edge and the slant height form a right triangle with the half-diagonal, we can apply the Pythagorean theorem.
Let's represent the base of the pyramid as a square of side length a, then the diagonal of the base will be a√2, and the length of r would be half of the diagonal, so r = (a√2)/2. Similarly, the slant height, s, the lateral edge, e, and the height, h, of the pyramid form a right triangle with e as the hypotenuse and h and r as the legs.
Applying the Pythagorean theorem:
e² = h² + r²
Plug in the given values to find r:
25² = h² + 24²
We can solve for r:
r = √(25² - 24²)
After obtaining r, we substitute back into the Pythagorean theorem to solve for h and get the height of the pyramid. The final answer should be rounded to the nearest whole number as per the student's request.