To apply the Pythagorean Theorem in this case, we can use the slant height, the height, and the base length as the legs of a right triangle. Let's call the base length x.
According to the Pythagorean Theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the slant height (25 ft), and the other two sides are the base length (x ft) and the height (h ft).
So, we have the equation: x^2 + h^2 = 25^2.
We also know that the base length is 40 ft, so we can substitute that into the equation: 40^2 + h^2 = 25^2.
Simplifying this equation, we have: 1600 + h^2 = 625.
Subtracting 625 from both sides, we get: h^2 = 975.
Taking the square root of both sides, we find: h ≈ 31.2 ft.
Therefore, the height of the square pyramid is approximately 31.2 ft.
The Pythagorean Theorem in Three Dimensions Quick Check
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Question
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.
15.0 ft.
15.0 ft.
32.0 ft.
3 answers
The Pythagorean Theorem in Three Dimensions Quick Check
2 of 52 of 5 Items
Question
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
54.4 cm
54.4 cm
51.2 cm
51.2 cm
46.6 cm
46.6 cm
59.5 cm
2 of 52 of 5 Items
Question
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
54.4 cm
54.4 cm
51.2 cm
51.2 cm
46.6 cm
46.6 cm
59.5 cm
To find the length of the diagonal of the rectangular prism (segment BE), we can use the Pythagorean Theorem.
Let's call the length of the diagonal BH as d.
We know that the length of the prism is 32 cm, the width is 24 cm, and the height is 44 cm. We are given that the length of the diagonal of the base, BH, is 40 cm.
We can consider the right triangle with one leg being the width (24 cm), the other leg being the height (44 cm), and the hypotenuse being the diagonal of the base (40 cm).
Using the Pythagorean Theorem, we have: width^2 + height^2 = diagonal of base^2.
So, 24^2 + 44^2 = 40^2.
Simplifying this equation, we get: 576 + 1936 = 1600.
Combining like terms, we have: 2512 = 1600.
Taking the square root of both sides, we find: d = √2512 ≈ 50.1 cm.
Therefore, the length of the diagonal of the rectangular prism BE is approximately 50.1 cm.
Let's call the length of the diagonal BH as d.
We know that the length of the prism is 32 cm, the width is 24 cm, and the height is 44 cm. We are given that the length of the diagonal of the base, BH, is 40 cm.
We can consider the right triangle with one leg being the width (24 cm), the other leg being the height (44 cm), and the hypotenuse being the diagonal of the base (40 cm).
Using the Pythagorean Theorem, we have: width^2 + height^2 = diagonal of base^2.
So, 24^2 + 44^2 = 40^2.
Simplifying this equation, we get: 576 + 1936 = 1600.
Combining like terms, we have: 2512 = 1600.
Taking the square root of both sides, we find: d = √2512 ≈ 50.1 cm.
Therefore, the length of the diagonal of the rectangular prism BE is approximately 50.1 cm.
5 answers