Question
25 ft.
h:
40 ft.
Apply the Pythagorean Theorem to determine the height of the square pyramid, h. Round the answer to the nearest tenth.
(1 point)
• 31.2 ft.
15.0 ft.
32.0 ft.
• 47.2 ft.
h:
40 ft.
Apply the Pythagorean Theorem to determine the height of the square pyramid, h. Round the answer to the nearest tenth.
(1 point)
• 31.2 ft.
15.0 ft.
32.0 ft.
• 47.2 ft.
Answers
GPT-4o mini
To determine the height \( h \) of the square pyramid using the Pythagorean theorem, we can visualize the pyramid's vertical height, the half of the base length, and the slant height.
In this case, the base of the pyramid is a square with each side length \( s \). Since no base length is given, we can take the half-length of one side of the base as \( \frac{s}{2} \).
The slant height (which is typically given) is represented in this case as 25 ft, and the vertical height of the pyramid is represented as \( h \).
The Pythagorean theorem is formulated as:
\[
a^2 + b^2 = c^2
\]
Where:
- \( a \) is the height \( h \),
- \( b \) is half of the base length \( \frac{s}{2} \),
- \( c \) is the slant height.
Given that the slant height is not directly identified with a specific base length, we assume a slant height of 40 feet (considered from the given options). Let's work through possible calculations; however, it appears there's been a mistake in identifying measurement values. The configurations of a pyramid typically would yield:
1. Slant height = 25 ft (given)
2. Height = \( h \).
3. Half of the base length to be determined.
If we assume for simplicity, the full base length is 40 ft, then:
\[
\left( \frac{40}{2} \right)^2 + h^2 = 25^2
\]
\[
20^2 + h^2 = 625
\]
Calculating \( 20^2 \):
\[
400 + h^2 = 625
\]
Subtracting 400 from both sides:
\[
h^2 = 625 - 400 = 225
\]
Taking the square root of \( 225 \):
\[
h = 15
\]
Given the original question options, the height \( h \) is approximately:
- **15.0 ft.**
Thus, the correct answer is **15.0 ft.**
In this case, the base of the pyramid is a square with each side length \( s \). Since no base length is given, we can take the half-length of one side of the base as \( \frac{s}{2} \).
The slant height (which is typically given) is represented in this case as 25 ft, and the vertical height of the pyramid is represented as \( h \).
The Pythagorean theorem is formulated as:
\[
a^2 + b^2 = c^2
\]
Where:
- \( a \) is the height \( h \),
- \( b \) is half of the base length \( \frac{s}{2} \),
- \( c \) is the slant height.
Given that the slant height is not directly identified with a specific base length, we assume a slant height of 40 feet (considered from the given options). Let's work through possible calculations; however, it appears there's been a mistake in identifying measurement values. The configurations of a pyramid typically would yield:
1. Slant height = 25 ft (given)
2. Height = \( h \).
3. Half of the base length to be determined.
If we assume for simplicity, the full base length is 40 ft, then:
\[
\left( \frac{40}{2} \right)^2 + h^2 = 25^2
\]
\[
20^2 + h^2 = 625
\]
Calculating \( 20^2 \):
\[
400 + h^2 = 625
\]
Subtracting 400 from both sides:
\[
h^2 = 625 - 400 = 225
\]
Taking the square root of \( 225 \):
\[
h = 15
\]
Given the original question options, the height \( h \) is approximately:
- **15.0 ft.**
Thus, the correct answer is **15.0 ft.**