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Chapter 5: Problem 44

Use Heron's Area Formula to find the area of the triangle. $$a=\frac{3}{5}, \quad b=\frac{5}{8}, \quad c=\frac{3}{8}$$

Short Answer

Expert verified
The area of the triangle is \(\frac{3}{32}\) square units.

Step by step solution

01

Calculate the Semi-Perimeter (s)

First you need to find the semi-perimeter of the triangle. The formula for this is \(s = \frac{(a + b + c)}{2}\). In this case, \(a = \frac{3}{5}\), \(b = \frac{5}{8}\), and \(c = \frac{3}{8}\). So, \(s = \frac{(\frac{3}{5} + \frac{5}{8} + \frac{3}{8})}{2} = \frac{69}{80}\).
02

Substitute into Heron's Formula

Now that you have the semi-perimeter, you can substitute the values into Heron's Formula: \(A = \sqrt{s(s - a)(s - b)(s - c)}\). Substituting the values and simplifying gives: \(A = \sqrt{\frac{69}{80} * (\frac{69}{80} - \frac{3}{5})(\frac{69}{80} - \frac{5}{8})(\frac{69}{80} - \frac{3}{8})} = \frac{3}{32}\).
03

Square Root the Result

Now, the final step is to take the square root of that multiplication result, which will give you the area: \(A = \sqrt{\frac{3}{32}} = \frac{3}{32}\) square units.

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