Question

2 multiple choice 1 point find the area of the triangle. a = 63 b = 50 c = 83.6 1571.43 2448.24 1569.63

Explanation:

Step1: Calculate the semi - perimeter \(s\)

The formula for the semi - perimeter of a triangle with sides \(a\), \(b\), and \(c\) is \(s=\frac{a + b + c}{2}\).
Substitute \(a = 63\), \(b = 50\), and \(c = 83.6\) into the formula:
\(s=\frac{63+50 + 83.6}{2}=\frac{196.6}{2}=98.3\)

Step2: Use Heron's formula to find the area \(A\)

Heron's formula is \(A=\sqrt{s(s - a)(s - b)(s - c)}\)
Substitute \(s = 98.3\), \(a = 63\), \(b = 50\), and \(c = 83.6\) into the formula:
\(A=\sqrt{98.3\times(98.3 - 63)\times(98.3 - 50)\times(98.3 - 83.6)}\)
\(=\sqrt{98.3\times35.3\times48.3\times14.7}\)
\(=\sqrt{98.3\times35.3\times(48.3\times14.7)}\)
\(=\sqrt{98.3\times35.3\times710.01}\)
\(=\sqrt{98.3\times(35.3\times710.01)}\)
\(=\sqrt{98.3\times25063.353}\)
\(=\sqrt{2463727.5}\approx1571.43\)

Answer:

1571.43