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Given:
The volume of a prism with equilateral triangular cross-section is 270cm³.
Length of the prism = cm
To find:
The length of the side of the equilateral triangular cross-section.
Solution:
Formulae used:
Area of an equilateral triangle is
Where a is the side length of equilateral triangle.
Volume of prism is
Where, B is base area and h is the height of the triangular prism.
Cross section of the prism is an equilateral triangular so the base area of the prism is sq. cm.
The volume of the prism is
Divide both sides by 7.5.
It takes only positive value because the side cannot be negative.
Therefore, the length of the side of the equilateral triangular cross-section is 6 cm.