Question

The mass of a triangular pyramid is 400 grams and the density of the material from which the pyramid is made is 16 g/cm3
. If the height of the pyramid is 5 centimeters, and the base of the pyramid is an equilateral triangle, which of the following correctly calculates its base side length?(1 point)
Responses

5.89 cm
5.89 cm

6.89 cm
6.89 cm

34.64 cm
34.64 cm

3.40 cm

Answer 1

Volume = mass/density = 400 ÷ 16 = 25 cm^3.
Base area = 3V/h = 3·25 ÷ 5 = 15 cm^2.
For an equilateral triangle, area = (√3/4) s^2, so s^2 = 4·15/√3 = 20√3, hence
s = √(20√3) ≈ 5.89 cm.

Answer: 5.89 cm.