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.
To find the height of the pyramid, we first need to find the length of the slant height. We can use the Pythagorean theorem to do this.
The formula for slant height (s) of a square pyramid is:
s = √(e^2 + h^2)
In this case, we know that e = 25 in. and s = 24 in., so we can substitute these values into the equation:
24 = √(25^2 + h^2)
To solve for h, we need to isolate it on one side of the equation. First, square both sides of the equation to eliminate the square root:
24^2 = (25^2 + h^2)
576 = 625 + h^2
Next, subtract 625 from both sides of the equation:
576 - 625 = h^2
-49 = h^2
To get rid of the squared term, we take the square root of both sides of the equation. Since we're looking for a positive height, we'll only consider the positive square root:
√(-49) = h
Since the square root of a negative number is not a real number, it means that there is no real height for this pyramid.