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)
Responses
31.2 ft.
31.2 ft.
47.2 ft.
47.2 ft.
15.0 ft.
15.0 ft.
32.0 ft.
32.0 ft.
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page 19 of 19
To apply the Pythagorean Theorem, we can use the right triangle formed by the height line, the slant height, and the part of the base edge where they meet.
Since the base edge has a length of 40 feet and the slant height is 25 feet, we can use the Pythagorean Theorem to solve for the height, h.
The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is the slant height (25 feet), and one of the sides is the base edge (40 feet). The other side is the height, h.
Using the Pythagorean Theorem, we can write:
h^2 + 40^2 = 25^2
Simplifying, we get:
h^2 + 1600 = 625
Subtracting 1600 from both sides, we get:
h^2 = 625 - 1600
h^2 = -975
Since we cannot take the square root of a negative number, we know that there is an error in the problem or the given values.
Therefore, we cannot determine the height of the square pyramid based on the given information.