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 The height of the square pyramid is?
To find the height of the square pyramid, we can use the Pythagorean theorem.
The lateral edge length, e, is the length of one side of the base, so the base of the square pyramid is a square with side length 25 in.
The slant height, s, is the height of one of the triangular faces, which is also the hypotenuse of a right triangle with e as one leg and h as the other leg.
Using the Pythagorean theorem, we have:
s^2 = e^2 + h^2
24^2 = 25^2 + h^2
576 = 625 + h^2
h^2 = 576 - 625
h^2 = -49
Since the height of a pyramid cannot be negative, there is no real solution for h^2 = -49.
Therefore, there is no height that satisfies the given values for e and s.
incorrect, try using Pythagorean theorem
Apologies for the confusion. Let's use the Pythagorean theorem to find the height of the pyramid.
The lateral edge length, e, is the length of one side of the base, so the base of the square pyramid is a square with side length 25 in.
The slant height, s, is the height of one of the triangular faces, and we can consider it as the hypotenuse of a right triangle with e as one leg and h as the other leg.
Using the Pythagorean theorem, we have:
s^2 = e^2 + h^2
24^2 = 25^2 + h^2
576 = 625 + h^2
Subtracting 625 from both sides of the equation:
h^2 = 576 - 625
h^2 = -49
Taking the square root of both sides (ignoring the negative solution):
h = √(-49)
Since the square root of a negative number is not real, there is no real solution for h in this case.
Therefore, there is no height that satisfies the given values for e and s.
find the height of a square pyramid . Each square pyramid's edge of the square base is 20 m and its slant height is 13.5 m.
To find the height of the square pyramid, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, we have a right triangle with the lateral edge (e) as one side and the slant height (s) as the hypotenuse. We want to find the height (h), which is the other side of the triangle.
Using the Pythagorean theorem, we have:
e^2 + h^2 = s^2
Substituting the known values, we get:
25^2 + h^2 = 24^2
625 + h^2 = 576
Now, let's solve for h:
h^2 = 576 - 625
h^2 = -49
Since we can't take the square root of a negative number, there is no real solution for h in this case.
Therefore, the height of the square pyramid cannot be found given the given lateral edge length (e) and slant height (s) values provided.