# Math Help - express the perimeter of triangle P as function of area A

1. ## express the perimeter of triangle P as function of area A

express the perimeter of triangle P as function of area A

2. ## Re: express the perimeter of triangle P as function of area A

This is impossible. All triangles with vertices at (n, 0), (-n, 0) and (0, 1/n) have area 1.

3. ## Re: express the perimeter of triangle P as function of area A

Hello, sluggerbroth!

Who asked this question? . . . It is stupid!

Express the perimeter of triangle $P$ as function of area $A$.
Code:
    - - - - * - - - - - - - - - - - - * - - - - - - - - - - - - * -
:      * *                      * *                      * *  :
:     *   *                   *   *                   *   *   :
3    *     *                *     *                *     *    3
:   *       *             *       *             *       *     :
:  *         *          *         *          *         *      :
- *  *  *  *  * - - - *  *  *  *  * - - - *  *  *  *  * - - - -
: - - 4 - - :       : - - 4 - - :       : - - 4 - - :
All these triangles have an area of 6 square units.

But obviously they have different perimeters.

So $P \:=\:f(6)\,$ has at least three possible values.
. . It is not a function.

4. ## Re: express the perimeter of triangle P as function of area A

How about $P=a+b+c$ and $A=\rho \cdot s$ where $\rho$ is the radius of the inscribed circle, and $s=\frac{a+b+c}{2}=\frac{P}{2}$. Now $P=\frac{2 A}{\rho}$. This can be considered a function in A (not just A, but A nevertheless).

5. ## Re: express the perimeter of triangle P as function of area A

This comes from Schaum’s Outlines Precalculus
It is a two part question and reads as follows:
A) Express the area A of equilateral triangle as function of one side s.
B) Express the perimeter of the triangle P as a function of the area A.

A) A(s)=(s squared )(square root 3)/4
and
B) P(A)=(6 square root A)/ (fourth root 3)

How to get to these answers???? HELP!!

6. ## Re: express the perimeter of triangle P as function of area A

Originally Posted by sluggerbroth
A) Express the area A of equilateral triangle as function of one side s.
You mislead people in this thread by omitting the word "equilateral." To answer this question, draw an altitude, which is also a median, and use the Pythagorean theorem to find its length.

7. ## Re: express the perimeter of triangle P as function of area A

I got part a of this but not part b B) Express the perimeter of the triangle P as a function of the area A.

How to get to this answer???? HELP!!

8. ## Re: express the perimeter of triangle P as function of area A

Originally Posted by sluggerbroth
I got part a of this but not part b B) Express the perimeter of the triangle P as a function of the area A.
So, P = 3s and you cannot express s through A from the equation $A=\frac{s^2\sqrt{3}}{4}$? Multiply both sides by $4/\sqrt{3}$ and takes the square root of both sides.