Question

a triangular prism has a lateral area of 285 square centimeters. its height is 19 centimeters and its base is an equilateral triangle. what is the length of each side of the triangle? centimeters

Explanation:

Step1: Recall the formula for lateral area of triangular prism

The lateral area \(L\) of a triangular prism is \(L = Ph\), where \(P\) is the perimeter of the base and \(h\) is the height of the prism.

Step2: Find the perimeter of the base

Given \(L = 285\) \(cm^{2}\) and \(h=19\) \(cm\). Using \(L = Ph\), we can find \(P\) by \(P=\frac{L}{h}\). Substitute the values: \(P=\frac{285}{19}=15\) \(cm\).

Step3: Find the side length of the equilateral triangle

Since the base is an equilateral triangle, and the perimeter \(P\) of an equilateral triangle is \(P = 3s\) (where \(s\) is the side - length). Then \(s=\frac{P}{3}\). Substitute \(P = 15\) \(cm\), we get \(s=\frac{15}{3}=5\) \(cm\).

Answer:

\(5\)