An illustration shows a square pyramid with labeled parts. The left, front, and right faces of the pyramid and base are visible. The back face is not visible, but its position is indicated by a dashed line. The back base edge is not visible, but its position is indicated by a dashed line. The left base edge is labeled a. The back left lateral edge is labeled e. A dotted line extends from the interior of the vertex straight down to the center of the base and is labeled h. A right angle is indicated where the dotted height line meets the base. Another dotted line extends from the center of the base where the height line meets to the center of the right base edge and is labeled r. A dotted line extends from the right base edge straight up the center of the right face of the prism and meets the height line at the vertex. The dotted slant height line is labeled s.
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 square pyramid, we need to first find the length of r.
The slant height s is the hypotenuse of a right triangle, with the lateral edge length e as one of the legs.
Using the Pythagorean theorem, we can find the length of the other leg, which is r.
s^2 = e^2 + r^2
24^2 = 25^2 + r^2
576 = 625 + r^2
r^2 = 576 - 625
r^2 = -49 (This is not possible since lengths cannot be negative)
Therefore, there is no real solution for r. Without the length of r, we cannot find the height of the pyramid.
To find the height of the pyramid, we first need to find the length of r.
Given that the lateral edge length e is 25 in. and the slant height s is 24 in., we can use the Pythagorean theorem to find r.
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (in this case, s) is equal to the sum of the squares of the other two sides (in this case, r and e).
So, we have:
s^2 = r^2 + e^2
Substituting the given values:
24^2 = r^2 + 25^2
Simplifying:
576 = r^2 + 625
Rearranging the equation:
r^2 = 576 - 625
r^2 = -49
Since we cannot have a negative length, we ignore this result and conclude that there is no solution for r. Therefore, we cannot find the length of h and subsequently the height of the pyramid with the given information.
To find the height of the pyramid, let's start by finding the length of the dotted line labeled "r".
We know that the lateral edge length, e, is 25 in. and the slant height, s, is 24 in.
Using the Pythagorean theorem, we can find the length of r:
r^2 = s^2 - e^2
r^2 = 24^2 - 25^2
r^2 = 576 - 625
r^2 = -49
From this calculation, we can see that r^2 is negative, which means there is an error in the given information. The square of a length cannot be negative.
Therefore, it is not possible to find the length of "r" and consequently we cannot find the height of the pyramid using the given information.