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=302
so 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.
