Question

Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 240 b = 122 c = 177

Answer 1

122 + 177 = 299
299 > 240  ⇒   triangle can be formed

Heron's formula:

$A= \sqrt{s(s-a)(s-b)(s-c)} \\ \\ s= \cfrac{a+b+c}{2}= \cfrac{240+122+177}{2}= 269.5 \\ \\ A= \sqrt{269.5(269.5-240)(269.5-122)(269.5-177)}= \\ = \sqrt{269.5*29.5*147.5*92.5}= \sqrt{108471223.4375} \approx 10414.952$