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 = 121 c = 302

Answer 1

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:

$s=\frac{a+b+c}{2}$

which is half of the perimeter of the triangle.

And the area formula itself:

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

we know that a=240, b=121 and c=302

so we can start by calculating s.

$s=\frac{a+b+c}{2}=\frac{240+121+302}{2}=331.5$

Once we got s, we can plug it into the given formula:

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

which yields:

$A=\sqrt{331.5(331.5-240)(331.5-121)(331.5-302)}$

when solving the parenthesis we get:

$A=\sqrt{331.5(91.5)(210.5)(29.5)}$

which simplifies to:

$A=\sqrt{188355689.4}$

so the answer is:

A=13 724.27 squared units.

Answer 2

These sides will form a triangle because the longest side (302) is less than the sum of the other 2 sides.  http://www.1728.org/trianinq.htm
Using Heron's formula, we first have to determine the semi-perimeter of the triangle.  (perimeter divided by 2)(240 + 121 + 302) / 2 = 331.50 = semi-perimeter (s)
Now, to use Heron's formula:area = square root (s • (s - a) • (s - b) • (s - c))area = square root (331.5 • (331.5 - a) • (331.5 - b) • (331.5 - c))area = square root (331.5 • (331.5 - 240) • (331.5 - 121) • (331.5 - 302))area = square root (331.5 • (331.5 - 240) • (331.5 - 121) • (331.5 - 302))area = square root (331.5 • (91.50) • (210.5) • (29.5))area = square root ( 188,355,689.44 )area = 13,724.27