1. ## Find Perimeter

If the area of a square is 9x^2 - 12xy + 4y^2, what is the perimeter of the square?

2. Originally Posted by magentarita
If the area of a square is 9x^2 - 12xy + 4y^2, what is the perimeter of the square?
Hi magentarita,

$\displaystyle 9x^2-12xy+4y^2$ can be factored into $\displaystyle (3x-2y)^2$

Now we know that the area of a square is $\displaystyle s^2$, where $\displaystyle s$ is one side.

That means that $\displaystyle s=3x-2y$

We have 4 of them, so $\displaystyle P=4(3x-2y)=12x-8y$

3. Hi

$\displaystyle 9x^2 - 12xy + 4y^2 = (3x-2y)^2$

Therefore the length of the sides is 3x-2y (or 2y-3x depending by the the sign of this quantity)

The perimeter is four times the length

4. ## Tell me...

Originally Posted by masters
Hi magentarita,

$\displaystyle 9x^2-12xy+4y^2$ can be factored into $\displaystyle (3x-2y)^2$

Now we know that the area of a square is $\displaystyle s^2$, where $\displaystyle s$ is one side.

That means that $\displaystyle s=3x-2y$

We have 4 of them, so $\displaystyle P=4(3x-2y)=12x-8y$
How do you factor this polynomial?

5. Originally Posted by masters
Hi magentarita,

$\displaystyle 9x^2-12xy+4y^2$ can be factored into $\displaystyle (3x-2y)^2$

$\displaystyle 9x^2 - 12xy + 4y^2$

$\displaystyle = (3x)^2 - 6xy-6xy +(2y)^2$

$\displaystyle =3x(3x-2y) - 2y(3x-2y)$

$\displaystyle =(3x-2y)(3x-2y) = (3x-2y)^2$

----------------------

You should remember the formula that

$\displaystyle a^2 - 2ab +b^2 = (a-b)^2$

Here a = 3x & b= 2y

6. Originally Posted by magentarita
How do you factor this polynomial?
To learn how to factor quadratics, try some online lessons. :wink:

7. ## thanks

$\displaystyle 9x^2 - 12xy + 4y^2$

$\displaystyle = (3x)^2 - 6xy-6xy +(2y)^2$

$\displaystyle =3x(3x-2y) - 2y(3x-2y)$

$\displaystyle =(3x-2y)(3x-2y) = (3x-2y)^2$

----------------------
You should remember the formula that

$\displaystyle a^2 - 2ab +b^2 = (a-b)^2$

Here a = 3x & b= 2y
Thank you for breaking down this question.