SOLUTION: A picture frame dimesions are 20cm by 30cm. If a mat was put inside the frame that decreases the picture area by 264cm^2, how wide is the mat?

Click here to see ALL problems on Quadratic Equations

Question 198912: A picture frame dimesions are 20cm by 30cm. If a mat was put inside the frame that decreases the picture area by 264cm^2, how wide is the mat?
Found 2 solutions by ankor@dixie-net.com, checkley75:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A picture frame dimensions are 20cm by 30cm. If a mat was put inside the frame
that decreases the picture area by 264cm^2, how wide is the mat?
:
Let x = width of the mat
:
Find the overall area of the picture and frame:
20 * 30 = 600 sq/cm
:
The dimension of the picture inside the mat
(20-2x)by(30-2x)
Foil to find the area:
A = 600 - 100x + 4x^2
:
Overall area - picture area = 264 sq/cm
600 - (4x^2 - 100x + 600) = 264
:
Remove the brackets (change signs) arrange as a quadratic eq
-4x^2 + 100x + 600 - 600 - 264 = 0
-4x^2 + 100x - 264 = 0
Multiply eq by -1
4x^2 - 100x + 264 = 0
Simplify divide by 4
x^2 - 25x + 66 = 0
Factor
(x - 22)(x - 3) = 0
Reasonable solution
x = 3 cm is the width of the mat
;
:
Check solution
Find the area of the picture (2x=6), subtract from the overall dimensions
14 * 24 = 336
then
600 - 336 = 264; confirms our solution

Answer by checkley75(3666) (Show Source):
You can put this solution on YOUR website!
(20-2X)(30-2X)=264
600-60X-40X+4X^2=264
4X^2-100X+600-264=0
4X^2-100X+336=0
4(X^2-25X+84)=0
4(X-21)(X-4)=0
X-21=0
X=21 ANS.
X-4=0
X=4 ANS.