Question
Look at the square pyramid below.
56 mi56\ \text{mi}56 mi lll
33 mi33\ \text{mi}33 mi
How many miles long is the slant height of the square pyramid? Click Here for Help Video.
16.5
16.5
56 mi56\ \text{mi}56 mi lll
33 mi33\ \text{mi}33 mi
How many miles long is the slant height of the square pyramid? Click Here for Help Video.
16.5
16.5
Answers
GPT-4o mini
To find the slant height of a square pyramid, we can use the relationship between the base, height, and slant height.
Given:
- The base of the square pyramid has a length of 56 miles.
- The height of the pyramid is 33 miles.
To find the slant height, we'll first establish the relationship:
1. The slant height (l) forms a right triangle with half of the base and the height of the pyramid.
2. The half of the base can be calculated as follows:
\[
\text{Half of the base} = \frac{56 \text{ mi}}{2} = 28 \text{ mi}
\]
3. Now we can apply the Pythagorean theorem, which states:
\[
l^2 = \text{height}^2 + \left(\text{half of the base}\right)^2
\]
Plugging in the values:
\[
l^2 = (33 \text{ mi})^2 + (28 \text{ mi})^2
\]
4. Calculating the squares:
\[
l^2 = 1089 + 784
\]
\[
l^2 = 1873
\]
5. Now, take the square root to find the slant height:
\[
l = \sqrt{1873} \approx 43.3 \text{ mi}
\]
Therefore, the slant height of the square pyramid is approximately \(43.3\) miles. If you intended to inquire about another measurement leading you to the answer \(16.5\), please provide additional context or parameters.
Given:
- The base of the square pyramid has a length of 56 miles.
- The height of the pyramid is 33 miles.
To find the slant height, we'll first establish the relationship:
1. The slant height (l) forms a right triangle with half of the base and the height of the pyramid.
2. The half of the base can be calculated as follows:
\[
\text{Half of the base} = \frac{56 \text{ mi}}{2} = 28 \text{ mi}
\]
3. Now we can apply the Pythagorean theorem, which states:
\[
l^2 = \text{height}^2 + \left(\text{half of the base}\right)^2
\]
Plugging in the values:
\[
l^2 = (33 \text{ mi})^2 + (28 \text{ mi})^2
\]
4. Calculating the squares:
\[
l^2 = 1089 + 784
\]
\[
l^2 = 1873
\]
5. Now, take the square root to find the slant height:
\[
l = \sqrt{1873} \approx 43.3 \text{ mi}
\]
Therefore, the slant height of the square pyramid is approximately \(43.3\) miles. If you intended to inquire about another measurement leading you to the answer \(16.5\), please provide additional context or parameters.