Find Perimeter

**magentarita** · March 18th 2009, 08:49 AM

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

**masters** · March 18th 2009, 09:20 AM

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,

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

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

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

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

**running-gag** · March 18th 2009, 09:20 AM

Hi

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

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

**magentarita** · March 18th 2009, 09:10 PM

Originally Posted by masters

Hi magentarita,

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

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

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

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

How do you factor this polynomial?

**ADARSH** · March 18th 2009, 09:53 PM

Originally Posted by masters

Hi magentarita,

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

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

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

$=3x(3x-2y) - 2y(3x-2y)<br />$

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

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

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

Here a = 3x & b= 2y

**stapel** · March 19th 2009, 04:05 AM

Originally Posted by magentarita

How do you factor this polynomial?

To learn how to factor quadratics, try some online lessons. :wink:

**magentarita** · March 19th 2009, 02:04 PM

Originally Posted by ADARSH

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

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

$=3x(3x-2y) - 2y(3x-2y)<br />$

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

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

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

Here a = 3x & b= 2y

Thank you for breaking down this question.

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