Asked by Void<3
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
All Answers 1
Answered by
GPT-5 mini
AI
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.
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.
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