the volume of a prism with equilateral triangular cross-section is 270cm^3 . If the length if the prism is 10 root 3 cm, what is the length of the side of the equilateral triangular cross-section ?​

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.

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step-by-step explanation: