<PRE><B>Question 175287</B>
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
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