For the square pyramid, the lateral edge length which is e 25 in., and the slant height, which is s , is 24 in. Find the height of the pyramid, which is h . Round the answer to the nearest whole number The height of the square pyramid is?

Question

For the square pyramid, the lateral edge length which is e 25 in., and the slant height, which is s , is 24 in. Find the height of the pyramid, which is h . Round the answer to the nearest whole number The height of the square pyramid is?

Answer 1

To find the height of the square pyramid, we can use the Pythagorean theorem.

The slant height, s, and the lateral edge length, e, form a right triangle with the height, h, as the hypotenuse.

Using the Pythagorean theorem, we have:

s^2 = e^2 + h^2

Substituting the given values, we have:

24^2 = 25^2 + h^2

576 = 625 + h^2

Rearranging the equation, we get:

h^2 = 576 - 625

h^2 = -49

Since we cannot take the square root of a negative number, this means that there is no real solution for the height of the pyramid in this case.

Therefore, the height of the square pyramid cannot be determined with the given information.

Answer 2

To find the height (h) of the square pyramid, we can use the Pythagorean theorem, since the slant height (s) and the lateral edge length (e) form a right triangle with the height as the hypotenuse.

Using the Pythagorean theorem:
h^2 = s^2 - (e/2)^2
h^2 = 24^2 - (25/2)^2
h^2 = 576 - 312.5
h^2 = 263.5

Taking the square root of both sides:
h = √263.5

Rounding to the nearest whole number:
h ≈ 16

The height of the square pyramid is approximately 16 inches.

Answer 3

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 hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the lateral edge length (e) of the pyramid is 25 in and the slant height (s) is 24 in. Let's use these values to find the height (h) of the pyramid:

We can set up a right triangle with the slant height (s) as the hypotenuse, the lateral edge length (e) as one of the legs, and the height (h) as the other leg.

Using the Pythagorean theorem, we have:
s² = e² + h²

Substituting the given values, we get:
24² = 25² + h²

Simplifying the equation, we have:
576 = 625 + h²

Now, let's solve for h:

h² = 576 - 625
h² = -49

Since we cannot have a negative value for the height, we can conclude that there is no real number solution to this equation. Therefore, we cannot find the height of the square pyramid using the given information.