To apply the Pythagorean Theorem, we can consider the right triangle formed by the height line, the slant height, and the base.
Let x be the length of the height line.
Let y be the length of the base.
Let z be the length of the slant height.
According to the Pythagorean Theorem, we have the equation:
x^2 + y^2 = z^2
Substituting the given values, we have:
x^2 + 40^2 = 25^2
x^2 + 1600 = 625
x^2 = 625 - 1600
x^2 = -975
Since the side lengths of a triangle cannot be negative, it means that there is no real solution to this equation. Therefore, we cannot determine the height of the square pyramid using the given information.
The correct answer is not given in the options.
Use the image to answer the question.
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. The back base edge is not visible but its position is indicated by a dashed line. The front base edge shows a length of 40 feet. 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. 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. This dotted line shows a slant height of 25 feet.
Apply the Pythagorean Theorem to determine the height of the square pyramid, h . Round the answer to the nearest tenth.
(1 point)
15.0 ft.
15.0 ft.
31.2 ft.
31.2 ft.
32.0 ft.
32.0 ft.
47.2 ft.
1 answer