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Chapter 5: Problem 63

Determine whether the statement is true or false. Justify your answer. In Heron's Area Formula, \(s\) is the average of the lengths of the three sides of the triangle.

Short Answer

Expert verified
The statement is false. In Heron's formula, \(s\) represents the semi-perimeter of the triangle, not the average of the lengths of the three sides.

Step by step solution

01

Understand Heron's Formula

Heron's formula allows you to calculate the area of a triangle if you know the length of all three sides. The formula is given as: \[ \sqrt{s(s-a)(s-b)(s-c)} \] where \(a\), \(b\), and \(c\) are the lengths of the sides of the triangle.
02

Decipher the variable 's'

The \(s\) in the formula is the semi-perimeter of the triangle. It is calculated as: \[ s = \frac{a + b + c}{2} \] where \(a\), \(b\), and \(c\) are lengths of the sides of the triangle.
03

Evaluate the statement

Here, \(s\) is not the average of the lengths of the three sides of the triangle, rather it is half of their sum which is the semi-perimeter of the triangle. Therefore, the statement is false.

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