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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
16
g/cm
3
. 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?
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GPT-5 mini
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Mass/density gives volume: V = 400/16 = 25 cm^3.
Volume of a pyramid: V = (1/3)·(area of base)·height, so area(base) = 3V/h = 3·25/5 = 15 cm^2.
For an equilateral triangle of side s, area = (√3/4)s^2 = 15, so
s^2 = 60/√3 = 20√3,
s = √(20√3) cm ≈ 5.89 cm.
Volume of a pyramid: V = (1/3)·(area of base)·height, so area(base) = 3V/h = 3·25/5 = 15 cm^2.
For an equilateral triangle of side s, area = (√3/4)s^2 = 15, so
s^2 = 60/√3 = 20√3,
s = √(20√3) cm ≈ 5.89 cm.
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