SOLUTION: Sheila has a picture frame that measures 20cm by 30cm. If she puts a mat inside the frame that decreases the picture area by 264cm2, how wide is the mat?

Question 175287: Sheila has a picture frame that measures 20cm by 30cm. If she puts a mat inside the frame that decreases the picture area by 264cm2, 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!
Sheila has a picture frame that measures 20cm by 30cm. If she puts a mat inside the frame that decreases the picture area by 264cm2, how wide is the mat?
:
Let x = the width of the matte around the picture
Then
Picture area: (20-2x) * (30-2x) = (600 - 100x + 4x^2) sq/cm
Overall frame area = 20 * 30 = 600 sq/c
:
Frame area - picture area = 264
600 - (600 - 100x + 4x^2) = 264
:
600 - 600 + 100x - 4x^2 = 264
:
0 = 4x^2 - 100x + 264
Simplify, divide eq by 4
x^2 - 25x + 66 = 0
Factors to:
(x-22)(x-3) = 0
Two solutions:
x = 22 cm
and
x = 3 cm, this is the one that makes sense
:
Check solution (subtract 2x which is 6 cm from the frame dimensions):
(20*30) - (14*24) =
600 - 336 = 264

Answer by checkley75(3666) (Show Source): You can put this solution on YOUR website!
20*30=600cm^2 is the picture area.
600-264=336
2x*3x=336
6x^2=336
x^2=336/6
x^2=56
x=sqrt56
x=7.48
2*7.48=14.96 for one dimention.
3*7.48=22.44 for the other dimention.
Proof:
14.96*22.44=336
336~336
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