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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

32.0 ft.
32.0 ft.

15.0 ft.
15.0 ft.

47.2 ft.
47.2 ft.

31.2 ft.
31.2 ft.
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Answer 1

To determine the height of the square pyramid, we can use the Pythagorean Theorem, which 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 of 25 feet, the base is 40 feet, and the height is represented by 'h'. Therefore, we can set up the following equation:

h^2 + 40^2 = 25^2

Simplifying this equation:

h^2 + 1600 = 625

Subtracting 1600 from both sides:

h^2 = 625 - 1600

h^2 = -975

Since the square of a length cannot be negative, this suggests that there is no real solution for the height of the square pyramid.

Answer 2

there has to be a solution because it doesn't give me the option of none

Answer 3

Apologies for the confusion. Let's re-evaluate the problem.

Using the Pythagorean Theorem, we have:

h^2 + 40^2 = 25^2

Simplifying further:

h^2 + 1600 = 625

Subtracting 625 from both sides:

h^2 = 625 - 1600

h^2 = -975

As the square of a length cannot be negative, it seems that there is no real solution for the height of the square pyramid in this case.

Answer 4

you are incorrect

Answer 5

Apologies for the mistake. Let's re-evaluate the problem.

Using the Pythagorean Theorem, we have:

h^2 + 40^2 = 25^2

Simplifying further:

h^2 + 1600 = 625

Subtracting 625 from both sides:

h^2 = 625 - 1600

h^2 = -975

Taking the square root of both sides to solve for h:

h = √(-975)

Since the square root of a negative number is not a real number, it appears that there is no real solution for the height of the square pyramid in this case.