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 \(A=\sqrt{s(s - a)(s - b)(s - c)}\)

Substitute \(s = 98.3\), \(a = 63\), \(b = 50\), and \(c = 83.6\) into Heron's formula:
\(A=\sqrt{98.3(98.3 - 63)(98.3 - 50)(98.3 - 83.6)}\)
\(=\sqrt{98.3\times35.3\times48.3\times14.7}\)
First, calculate \(98.3\times35.3 = 98.3\times(35+0.3)=98.3\times35+98.3\times0.3=3440.5+29.49 = 3469.99\)
\(48.3\times14.7=(50 - 1.7)\times14.7=50\times14.7-1.7\times14.7=735 - 24.99 = 710.01\)
Then \(3469.99\times710.01\approx3470\times710 = 2463700\)
\(A=\sqrt{2463700}\approx1571.43\)

Answer:

1571.43