Find the slant height of the square pyramid. Round to the nearest whole inch, if necessary.
(1 point)
Responses
13 in.
13 in.
15 in.
15 in.
6 in.
6 in.
8 in.
There is not enough information provided to find the slant height of the square pyramid.
To find the slant height of a square pyramid, we can use the Pythagorean theorem. The slant height can be found by finding the hypotenuse of a right triangle formed by the height of the pyramid and half the length of the base.
Let's assume the height of the pyramid is 13 in and the length of the base is 8 in.
Using the Pythagorean theorem, we have:
Slant height = √(height^2 + (base/2)^2)
Slant height = √(13^2 + (8/2)^2)
Slant height = √(169 + 16)
Slant height = √185
Slant height ≈ 13.60 in
Rounded to the nearest whole inch, the slant height of the square pyramid is 14 in.
To find the slant height of a square pyramid, we need to know the length of the pyramid's diagonal and the length of the side of the square base. From the given answer options, we can see that there are four options: 13 in, 15 in, 6 in, and 8 in.
To determine the correct answer, we need to use the Pythagorean theorem. In a square pyramid, the slant height, side length of the square base, and diagonal form a right triangle.
Let's check each option using the Pythagorean theorem:
1. For the option 13 in:
If the diagonal is 13 in and the side length of the square base is x, we can use the Pythagorean theorem to find the slant height:
x^2 + x^2 = 13^2
2x^2 = 169
x^2 = 169/2
x ≈ 10.4 (not a whole number, so this option is incorrect)
2. For the option 15 in:
If the diagonal is 15 in and the side length of the square base is x, we can use the Pythagorean theorem to find the slant height:
x^2 + x^2 = 15^2
2x^2 = 225
x^2 = 225/2
x ≈ 10.6 (not a whole number, so this option is incorrect)
3. For the option 6 in:
If the diagonal is 6 in and the side length of the square base is x, we can use the Pythagorean theorem to find the slant height:
x^2 + x^2 = 6^2
2x^2 = 36
x^2 = 18
x ≈ 4.2 (not a whole number, so this option is incorrect)
4. For the option 8 in:
If the diagonal is 8 in and the side length of the square base is x, we can use the Pythagorean theorem to find the slant height:
x^2 + x^2 = 8^2
2x^2 = 64
x^2 = 32
x ≈ 5.7 (not a whole number, so this option is incorrect)
Based on the calculations above, none of the given options are correct. Please check the problem and available answer choices again.