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
47.2 ft.
47.2 ft.
31.2 ft.
31.2 ft.
32.0 ft.
32.0 ft.
15.0 ft.
To apply the Pythagorean Theorem to determine the height of the square pyramid, we can use the relationship between the slant height and the height.
According to the Pythagorean Theorem, 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 slant height (25 feet) is the hypotenuse and the height (h) is one of the other two sides. The base of the triangle formed by the slant height and the height is the distance from the center of the base to the center of the right base edge, which is half the length of the front base edge (40 feet/2 = 20 feet).
Using the Pythagorean Theorem, we can set up the equation:
h^2 + 20^2 = 25^2
Simplifying:
h^2 + 400 = 625
h^2 = 625 - 400
h^2 = 225
Taking the square root of both sides:
h = √225
h = 15 feet
Therefore, the height of the square pyramid is 15 feet.
The correct answer is: 15.0 ft.
To apply the Pythagorean Theorem and determine the height of the square pyramid, you need to use the given measurements of the slant height and the length of the base.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In the illustration, the slant height of the pyramid is given as 25 feet, and the length of the base is given as 40 feet. These two sides form a right triangle with the height line as the hypotenuse.
To find the height, h, we can use the Pythagorean Theorem equation:
h^2 = slant height^2 - base length^2
Substituting the given values:
h^2 = 25^2 - 40^2
h^2 = 625 - 1600
h^2 = -975
Since the height cannot be negative, we can conclude that there is no real solution for the height of the square pyramid using these measurements.
To determine the height of the square pyramid using the Pythagorean Theorem, we can use the given information about the slant height and the length of the base.
The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides.
In this case, the slant height of 25 feet is the hypotenuse of a right triangle, and the height we are trying to find is one of the other sides.
Let's call the height "h" and the side of the base "b".
According to the Pythagorean Theorem, we have:
h^2 + (b/2)^2 = 25^2
Since the front base edge length is given as 40 feet, the side of the base (b) is 40 feet.
h^2 + (40/2)^2 = 25^2
Simplifying the equation, we have:
h^2 + 20^2 = 25^2
h^2 + 400 = 625
Subtracting 400 from both sides:
h^2 = 225
Taking the square root of both sides, we get:
h = √225
h = 15 feet
Therefore, the height of the square pyramid (h) is 15 feet.
Use the image to answer the question.
An illustration of a rectangular prism is shown with labeled parts. The left and back base edges are not visible but their positions are indicated by a dashed line. The 6 vertices are labeled A B C D E F and G. The base edge A B is labeled length. Base edge B C is labeled width. The perpendicular C D is labeled height. A dotted line crosses the rectangular base through the center to show diagonal B H. A dashed line extends up from the base indicating the left rear perpendicular E H. A dotted line crosses from the back top left vertex E to the front bottom right vertex B to show diagonal B E. This dotted line is labeled diagonal.
The length of the prism is 32 cm, the width is 24 cm, the height is 44 cm, and the length of the diagonal of the base, segment BH , is 40 cm. Find the length of the diagonal of the rectangular prism, segment BE . Round the answer to the nearest tenth.
(1 point)
Responses
51.2 cm
51.2 cm
54.4 cm
54.4 cm
59.5 cm
59.5 cm
46.6 cm
46.6 cm