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) The height of the square pyramid is in.
To find the height of the pyramid, we need to find the length of r, which represents the base diagonal.
Using the Pythagorean theorem, we can find the length of r:
r^2 = (e/2)^2 + h^2 (where e is the edge length and h is the height)
Plugging in the given values:
r^2 = (25/2)^2 + h^2 = 625/4 + h^2
Next, we can use the slant height to find the length of r:
s^2 = (e/2)^2 + r^2
Plugging in the given values:
24^2 = (25/2)^2 + r^2
576 = 625/4 + r^2
576 - 625/4 = r^2
(2304 - 625)/4 = r^2
1679/4 = r^2
Now we can set the two expressions for r^2 equal to each other:
625/4 + h^2 = 1679/4
Combining like terms:
h^2 = 1679/4 - 625/4
h^2 = 1054/4
h^2 = 263.5
Taking the square root of both sides:
h = √(263.5)
Rounding to the nearest whole number:
h ≈ 16
Therefore, the height of the square pyramid is approximately 16 inches.
try agian
Apologies for the mistake. Let's calculate the height again.
We know that the slant height, s, is 24 in. and the lateral edge length, e, is 25 in.
We can find the base diagonal, r, using the Pythagorean theorem:
r^2 = (e/2)^2 + s^2
r^2 = (25/2)^2 + 24^2
r^2 = 625/4 + 576
r^2 = 625/4 + 2304/4
r^2 = 2929/4
Now, let's calculate the height, h, by using the formula:
h^2 = r^2 - (e/2)^2
h^2 = 2929/4 - (25/2)^2
h^2 = 2929/4 - 625/4
h^2 = 2304/4
h^2 = 576
Therefore, the height of the square pyramid is 24 inches when rounded to the nearest whole number.
rong
Apologies again for the mistake. Let's try another approach to find the height.
We know that the slant height, s, is 24 in. and the lateral edge length, e, is 25 in.
Using the Pythagorean theorem, we can find the height, h, by considering a right triangle formed by the height, the slant height, and the radius of the base.
We have:
r^2 = (e/2)^2 + h^2
Substituting the given values:
r^2 = (25/2)^2 + h^2
r^2 = 625/4 + h^2
We can also use the slant height, s, and the radius, r, to form another right triangle:
s^2 = r^2 + h^2
Substituting the given values:
24^2 = r^2 + h^2
Now, we can equate these two expressions for r^2:
625/4 + h^2 = r^2
r^2 = r^2 + h^2 - 576
Simplifying:
625/4 + h^2 = h^2 - 576
625/4 = - 576
This equation does not have a solution. It seems that there is an error in the given information or the problem statement.
Please double-check the values provided or let me know if there is any additional information.
To find the height of the square pyramid, we need to first find the length of the slant height (s) and the lateral edge length (e).
From the given information, we have:
Lateral edge length (e) = 25 in.
Slant height (s) = 24 in.
To find the length of the height (h), we can use the Pythagorean Theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (also known as the hypotenuse).
In this case, the slant height (s) is the hypotenuse, the lateral edge length (e) is one of the shorter sides, and the height (h) is the other shorter side.
Using the Pythagorean Theorem, we can write the equation:
s^2 = e^2 + h^2
Substituting the given values:
24^2 = 25^2 + h^2
Simplifying this equation:
576 = 625 + h^2
Rearranging the equation to solve for h^2:
h^2 = 576 - 625
h^2 = -49
At this point, we encounter a problem. The result is a negative value, which means that there is no real solution for the height (h) of the pyramid using the given dimensions.
Therefore, it is not possible to find the height of the square pyramid with the given information.