Question 134122
The total area including the frames border is 34*17 or 578 cm^2

The area of the border alone is 578-318=260 cm^2

If you draw a picture, you may be able to follow what I'm doing

Area of the border=2(34*x)+2x(17-2x) and this equals

68x+34x -4x^2and we know that this equals 260 cm^2

-4x^2+102x-260=0  divide each term by -2
2x^2-51x+130=0-------------------quadratic in standard form

Another way to arrive at this quadratic is to realize that the length and width of the picture that's showing is (34-2x) and (17-2x) and we know that 

(34-2x)(17-2x)=318 expanding, using FOIL, we get:
578-68x-34x+4x^2=318  subtract 318 from each side

578-318-102x+4x^2=318-318  collecting like terms
260-102x+4x^2=0  divide each term by 2

2x^2-51x+130=0-----------quadratic in standard

Can you solve using the quadratic formula?
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{x = (51 +- sqrt( (-51)^2-4*2*130 ))/(2*2) }}} 
{{{x = (51 +- sqrt(2601-1040 ))/(4) }}} 
{{{x = (51 +- sqrt(1561))/(4) }}} 
{{{x = (51 +- 39.509)/(4) }}} 
{{{x = (51 +39.509)/(4) }}} 
{{{x=22.627}}} cm  DOESN'T WORK---LEADS TO NEGATIVE VALUE FOR AREA
and
{{{x = (51- 39.509)/(4) }}} 
{{{x=2.872}}} cm

CK
(34-2x)(17-2x)=318
34-2*2.872)(17-2*2.872)=318
28.255*11.256=318
~~~~~~318=318

Hope this helps--ptaylor