Use the image to answer the question. The image depicts a square pyramid that on the top right side has a arrow pointing to 25 ft. And on the bottom side has 40 ft written beneath it. Also in the middle of it there is an h. Apply the pythagorean theorem to determine the height of the square. Pyramid, h. Round the answer to the nearest 10th. The available responses are: 15.0 ft. 31.2 ft. 32.0 ft. Or 47.2 ft.

Answer 1

To find the height of the square pyramid, we can use the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse (h) is equal to the sum of the squares of the other two sides.

Let x be the side length of the square base of the pyramid.

Using the information given:
x^2 + (1/2 * x)^2 = 40^2
x^2 + (1/4)x^2 = 1600
1.25x^2 = 1600
x^2 = 1600 / 1.25
x^2 = 1280
x = sqrt(1280)
x ≈ 35.8 ft

Now, we can find the height h using the same method:
h^2 = 25^2 + (35.8)^2
h^2 = 625 + 1280
h^2 = 1905
h = sqrt(1905)
h ≈ 43.7 ft

Rounded to the nearest 10th, the height of the square pyramid is approximately 43.7 ft. Since this is not one of the available responses, we can assume there is a mistake in my calculations or the given responses.