of 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
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 longest side) is equal to the sum of the squares of the other two sides.
In this case, the lateral edge length (e) is one side of the right triangle, the slant height (s) is the hypotenuse, and the height (h) is the other side.
We can set up the equation:
e^2 + h^2 = s^2
Substituting in the given values:
25^2 + h^2 = 24^2
625 + h^2 = 576
h^2 = 576 - 625
h^2 = -49
Since the height cannot be a negative value, it means that the given measurements are not possible for a square pyramid.
To find the height of the square pyramid, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the slant height, s) is equal to the sum of the squares of the other two sides.
In this case, the slant height (s) is 24 in, and the lateral edge length (e) is given as 25 in. Let's consider the right triangle formed by the slant height, height (h), and half the base of the square pyramid.
Using the Pythagorean theorem, we have:
s^2 = h^2 + (e/2)^2
Plugging in the values we have:
24^2 = h^2 + (25/2)^2
576 = h^2 + 12.5^2
576 = h^2 + 156.25
Rearranging the equation:
h^2 = 576 - 156.25
h^2 = 419.75
Taking the square root of both sides:
h ≈ √419.75
h ≈ 20.49
Rounding the answer to the nearest whole number, the height of the pyramid is approximately 20 inches.
To find the height of the square pyramid, we can use the Pythagorean theorem.
In a square pyramid, the slant height (s) is the hypotenuse of a right triangle formed by half the base length (e/2), the height (h), and the slant height (s).
Using the Pythagorean theorem, we have:
(s)^2 = (e/2)^2 + (h)^2
In this case, given that the lateral edge length (e) is 25 in and the slant height (s) is 24 in, we can substitute these values into the equation to solve for the height (h):
(24)^2 = (25/2)^2 + (h)^2
576 = (625/4) + (h)^2
To simplify, we can multiply 625/4 by 4/4 to get a common denominator:
576 = (625/4) + (h)^2
576 = 2500/4 + (h)^2
576 = 625 + (h)^2
Now we can isolate (h)^2 by subtracting 625 from both sides:
576 - 625 = (h)^2
-49 = (h)^2
To get rid of the square, take the square root of both sides (remembering to consider both the positive and negative square root):
sqrt(-49) = sqrt((h)^2)
As the square root of a negative number is not a real number, there is no valid solution for the height (h) of the square pyramid in this case.