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 . (1 point)
To find the height of the pyramid, we need to find the length of the slant height, r.
We can use the Pythagorean theorem to find the length of r:
r^2 = s^2 - e^2
r^2 = 24^2 - 25^2
r^2 = 576 - 625
r^2 = -49
Since r is the length of a line, it cannot be negative. Therefore, there is no solution for r^2 = -49.
Therefore, the given dimensions for e and s are not possible for a square pyramid.
give the closest answer
Apologies for the confusion. Let's assume that the dimensions are possible and proceed with finding the height of the pyramid.
Given:
Lateral edge length (e) = 25 in.
Slant height (s) = 24 in.
To find the height of the pyramid (h), we can use the Pythagorean theorem:
s^2 = h^2 + r^2
Plugging in the values we have:
24^2 = h^2 + 25^2
576 = h^2 + 625
h^2 = 576 - 625
h^2 = -49
Again, we have obtained a negative value for h^2. However, height cannot be negative, so there must be an error in the given values. Please double-check the dimensions provided.
To find the height of the square pyramid, we need to first find the length of the base diagonal (r).
We can use the Pythagorean theorem to find the length of r:
r^2 = e^2 + s^2
r^2 = 25^2 + 24^2
r^2 = 625 + 576
r^2 = 1201
To find r, we take the square root of both sides:
r = √1201
Next, we can find the height (h) using the Pythagorean theorem again.
h^2 = s^2 - (r/2)^2
h^2 = 24^2 - (r/2)^2
h^2 = 576 - (r^2/4)
h^2 = 576 - 1201/4
h^2 = 576 - 300.25
h^2 = 275.75
To find h, we take the square root of both sides:
h = √275.75
Finally, we can round the value of h to the nearest whole number:
h ≈ 17
Therefore, the height of the square pyramid is approximately 17 inches.