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 = 121 c = 302

Answer:Yes, the triangle can be formed with the given side lengths and it would have an area of 13,724.27 squared units.Step-by-step explanation:So first, yes, a triangle can be formed because the sum of the smaller sides is greater than the biggest side.So first, Heron's formula consists on two parts:[tex]s=\frac{a+b+c}{2}[/tex]which is half of the perimeter of the triangle.And the area formula itself:[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]we know that a=240, b=121 and c=302so we can start by calculating s.[tex]s=\frac{a+b+c}{2}=\frac{240+121+302}{2}=331.5[/tex]Once we got s, we can plug it into the given formula:[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]which yields:[tex]A=\sqrt{331.5(331.5-240)(331.5-121)(331.5-302)}[/tex]when solving the parenthesis we get:[tex]A=\sqrt{331.5(91.5)(210.5)(29.5)}[/tex]which simplifies to:[tex]A=\sqrt{188355689.4}[/tex]so the answer is:A=13 724.27 squared units.