A square pyramid with slant height s, drawn on the right triangle side. Vertical, perpendicular height, h, of the pyramid drawn from the vertex to the base. Side length of square base labeled with upper L.

Question

In the square pyramid, the perpendicular height, h, equals 125 meters. The side length, L, is equal to 100 meters. What is the slant height, s, to the nearest tenth?

(1 point)
Responses

160.1 m.
160.1 m.

13.2 m.
13.2 m.

134.6 m.
134.6 m.

15 m.

Answer 1

To find the slant height \( s \) of the square pyramid, we can use the Pythagorean theorem. The slant height, the perpendicular height, and half the side length of the base form a right triangle.

1. Identify the sides of the triangle:

   • Half the side length of the base \( L = 100 , \text{m} \).
   • Half of \( L \) is \( \frac{L}{2} = \frac{100}{2} = 50 , \text{m} \).
   • The perpendicular height \( h = 125 , \text{m} \).

2. Apply the Pythagorean theorem: \[ s^2 = h^2 + \left(\frac{L}{2}\right)^2 \] \[ s^2 = 125^2 + 50^2 \] \[ s^2 = 15625 + 2500 = 18125 \] \[ s = \sqrt{18125} \]

3. Calculate \( s \): \[ s \approx 134.6 , \text{m} \]

Thus, the slant height \( s \) to the nearest tenth is 134.6 m.

The correct response is: 134.6 m.