Question

decide whether a triangle can be formed. if so, find its area.

1. a = 73, b = 94, c = 83.6

Explanation:

Step1: Check triangle inequality

Check \(a + b>c\), \(a + c>b\), \(b + c>a\).
\(73+94 = 167>83.6\), \(73 + 83.6=156.6>94\), \(94+83.6 = 177.6>73\). So a triangle can be formed.

Step2: Calculate semi - perimeter \(s\)

\(s=\frac{a + b + c}{2}=\frac{73+94 + 83.6}{2}=\frac{250.6}{2}=125.3\)

Step3: Use Heron's formula \(A=\sqrt{s(s - a)(s - b)(s - c)}\)

\(A=\sqrt{125.3(125.3 - 73)(125.3 - 94)(125.3 - 83.6)}\)
\(=\sqrt{125.3\times52.3\times31.3\times41.7}\)
First calculate \(125.3\times52.3 = 6553.19\), \(31.3\times41.7=1305.21\)
Then \(6553.19\times1305.21\approx8.55\times10^{6}\)
\(A=\sqrt{8.55\times 10^{6}}\approx2924\)

Answer:

A triangle can be formed and its area is approximately \(2924\)