Find the slant height of the square pyramid.
16 15
To find the slant height of a square pyramid, we typically need two pieces of information: the height of the pyramid and the length of one side of the base, which is square.
The two numbers you've provided (16 and 15) must correspond to these measures, though you haven't specified which is which. However, because we are dealing with a square pyramid, we can assume the larger number is the slant height, because in a right square pyramid, the slant height is always longer than the half-diagonal of the base and the vertical height.
So, if 16 is the slant height, then we have the slant height already, and that's the answer.
However, if you meant that 16 is the side of the base and 15 is the height of the pyramid, or vice versa, we would calculate the slant height using the Pythagorean theorem for the right triangle formed by the height (h), the half-diagonal of the base (d/2), and the slant height (l).
Let's assume that 16 is the side of the base (s), and 15 is the height of the pyramid (h). The half-diagonal of the base (d/2) would be calculated using the Pythagorean theorem for the square base's half-diagonal because we know that for a square with sides of length s, the diagonal (d) is s√2. Thus, the half-diagonal of the base (d/2) is (s√2)/2.
Let's calculate the half-diagonal of the base for a side length of 16:
d/2 = (16√2)/2 = 8√2
Now, using the Pythagorean theorem (a^2 + b^2 = c^2) where a is the height of the pyramid, b is the half-diagonal of the base, and c is the slant height (l), we can solve for the slant height:
15^2 + (8√2)^2 = l^2
225 + (8√2)^2 = l^2
225 + 128 = l^2
353 = l^2
Now, let's take the square root of both sides to solve for l:
l = √353
This would be the slant height given that 16 is the side of the base and 15 is the height of the pyramid.
Be aware that if the pyramid is not a right pyramid (meaning the apex is not directly above the center of the base), the calculation would be incorrect. The method described above is for a right square pyramid only.
Answer
If 16 is the slant height of the square pyramid, then the slant height is simply:
Slant height (l) = 16 units