Find the slant height of the square pyramid. Round to the nearest whole inch, if necessary. (1 point) Responses 6 in. 6 in. 8 in. 8 in. 15 in.
The slant height of a square pyramid can be found using the Pythagorean theorem, with the height of the pyramid, h, and the length of one side of the base, s, as the legs of the right triangle.
Let's assume the height of the pyramid is h, the length of one side of the base is s, and the slant height is L.
Using the Pythagorean theorem, the equation can be written as:
L^2 = h^2 + (s/2)^2
Since it is a square pyramid, the length of one side of the base, s, is equal to the length of the other sides of the square base.
From the given responses, we can try substituting each value:
For 6 inches: L^2 = h^2 + (6/2)^2
L^2 = h^2 + 3^2
L^2 = h^2 + 9
For 8 inches: L^2 = h^2 + (8/2)^2
L^2 = h^2 + 4^2
L^2 = h^2 + 16
For 15 inches: L^2 = h^2 + (15/2)^2
L^2 = h^2 + 225/4
Since both 6 inches and 8 inches round to whole numbers, they could be possible answers. However, without any further information, we cannot determine the exact value of the slant height L. Therefore, the best answer from the given options would be 6 in.