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
15.0 ft.
15.0 ft.
32.0 ft.
32.0 ft.
31.2 ft.
31.2 ft.
47.2 ft.
47.2 ft.
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To apply the Pythagorean Theorem, we can use the equation:
c^2 = a^2 + b^2,
where c is the slant height (25 feet) and a and b are the other two sides of the right triangle formed by the height line.
Let's call the height "h" and one side of the base "x". Since the base is a square, all sides are equal, so the other side of the base is also "x".
Using the Pythagorean Theorem, we can set up the equation:
25^2 = x^2 + h^2.
We also know that the length of the base (x) is 40 feet.
Now we can substitute these values into the equation:
25^2 = 40^2 + h^2.
Simplifying this equation, we have:
625 = 1600 + h^2.
Subtracting 1600 from both sides, we get:
h^2 = 625 - 1600.
Simplifying further, we have:
h^2 = -975.
Since the height of a pyramid cannot be negative, we can conclude that there is no real solution to this equation.
Therefore, the height of the square pyramid cannot be determined.