SOLUTION: a picture frame measures 34cm by 17cm. There is a 318cm^2 of picture showing. The frame is uniform thickness. Find the thickness of thr frame.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: a picture frame measures 34cm by 17cm. There is a 318cm^2 of picture showing. The frame is uniform thickness. Find the thickness of thr frame.      Log On


   

Question 134122: a picture frame measures 34cm by 17cm. There is a 318cm^2 of picture showing. The frame is uniform thickness. Find the thickness of thr frame.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
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+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%2851+%2B-+sqrt%28+%28-51%29%5E2-4%2A2%2A130+%29%29%2F%282%2A2%29+
x+=+%2851+%2B-+sqrt%282601-1040+%29%29%2F%284%29+
x+=+%2851+%2B-+sqrt%281561%29%29%2F%284%29+
x+=+%2851+%2B-+39.509%29%2F%284%29+
x+=+%2851+%2B39.509%29%2F%284%29+
x=22.627 cm DOESN'T WORK---LEADS TO NEGATIVE VALUE FOR AREA
and
x+=+%2851-+39.509%29%2F%284%29+
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