For the square pyramid the lateral edge length is 25 in. and the slant height is 24 in. Find the height of the pyramid 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.
In a square pyramid, the slant height is the hypotenuse of a right triangle, with one leg being the lateral edge length and the other leg being half the length of one side of the square base.
Let's set up the equation using the Pythagorean theorem:
lateral edge length = 25 in.
slant height = 24 in.
side length of the square base = ?
Since the slant height is the hypotenuse, and one leg of the triangle is the lateral edge length, we can use the formula:
slant height^2 = lateral edge length^2 + (side length of the square base / 2)^2
Substituting the given values:
24^2 = 25^2 + (side length of the square base / 2)^2
Simplifying the equation:
576 = 625 + (side length of the square base / 2)^2
Rearranging the equation to isolate (side length of the square base / 2)^2:
(side length of the square base / 2)^2 = 576 - 625
(side length of the square base / 2)^2 = -49
Since the square of any real number cannot be negative, we can conclude that there is no solution to this equation. Therefore, there is no height for the given lateral edge length and slant height.
Please double-check the given measurements to ensure correctness and try solving the problem again.
To find the height of the square pyramid, we can use the Pythagorean Theorem.
The lateral edge length is 25 in, and the slant height is 24 in. Let the height of the pyramid be represented by "h".
Using the Pythagorean Theorem, we have:
25^2 = h^2 + 24^2
625 = h^2 + 576
h^2 = 625 - 576
h^2 = 49
Taking the square root of both sides, we find:
h = sqrt(49) = 7
Therefore, the height of the square pyramid is 7 inches.
To find the height of the square pyramid, we can use the Pythagorean theorem.
The lateral edge length of the pyramid is 25 in, and the slant height is 24 in.
Let's represent the height of the pyramid as 'h'.
Using the Pythagorean theorem, we can set up the equation:
h^2 + (25/2)^2 = 24^2
Simplifying, we get:
h^2 + (625/4) = 576
Subtracting (625/4) from both sides:
h^2 = 576 - (625/4)
Convert 576 to a fraction with a denominator of 4:
h^2 = (2304/4) - (625/4)
Combining the fractions:
h^2 = 1679/4
Taking the square root of both sides:
h = √(1679/4)
Calculating the square root of 1679/4:
h ≈ 20.6
Rounding to the nearest whole number:
The height of the square pyramid is approximately 21 inches.