Heron's formula

[Bess]

How to separate the variable c from the heron formula?
A= s(s−a)(s−b)(s−c) all this in square roots

 

[topsquark]

[math]A = \sqrt{s(s - a)(s - b)(s - c)}[/math] where [math]s = \dfrac{1}{2} ( a + b + c)[/math]
This is going to give you a quartic equation in c. Very messy to work with. All I can suggest is to put the value for s into the area formula and start multiplying out. There will be a little symmetry to help you out but it's going to be ugly.

Here's the four solutions.

-Dan

 

[Bess]

[QUOTE = "topsquark, postimi: 522759, anëtar: 31690"]
[matematikë] A = \ sqrt {s (s - a) (s - b) (s - c)} [/ matematikë] ku [matematikë] s = \ dfrac {1} {2} (a + b + c) [/ matematikë]

Kjo do t'ju japë një ekuacion kuartik në c. Shumë i çrregullt për të punuar. E tëra që mund të sugjeroj është të vendos vlerën për s në formulën e zonës dhe të fillojë të shumëzohet. Do të ketë një simetri të vogël për t'ju ndihmuar, por do të jetë e shëmtuar.

Këtu janë katër zgjidhjet.

-Dan
[/ QUOTE]
thank you

 

[Dr.Peterson]

How to separate the variable c from the heron formula?
A= s(s−a)(s−b)(s−c) all this in square roots

It is possible that there is a simpler way to solve whatever you are ultimately trying to do. Can you tell us why you want to solve this formula for c, and what the larger problem is that this is a part of? What are you taking as known, and what is your ultimate goal?

 

[HallsofIvy]

Heron's formula finds the area of a triangle with side lengths a, b, and c and s is the "half perimeter", s= (a+ b+ c)/2. s is also a length so all four are units of length (feet, yards, meters, centimeters, etc.) Then, of course all four of s, s- a, s- b, and s- c have units of length also. That means that s(s- a)(s- b)(s- c) has units of "length to the fourth power".

But area always has units of "length square" (square feet, square yards, square meters, square centimeters, etc.). That is why the square root is needed:
\(\displaystyle A= \sqrt{s(s- a)(s- b)(s- c)}\).