SOLUTION: An 8 dm by 6 dm picture is to be photocopied in reduced size. The owner wants the copy to be half the size of the original picture. If the length and the width of the original pict

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Question 636231: An 8 dm by 6 dm picture is to be photocopied in reduced size. The owner wants the copy to be half the size of the original picture. If the length and the width of the original picture will be reduced by the same measure, find the dimension of the photocopy.
Answer by ankor@dixie-net.com(15746) About Me  (Show Source):
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An 8 dm by 6 dm picture is to be photocopied in reduced size.
The owner wants the copy to be half the size of the original picture.
If the length and the width of the original picture will be reduced by the
same measure, find the dimension of the photocopy.
:
Find the area of the original: 8 * 6 = 48 sq/dm
Assume half the size means half the area: 24 sq/dm
Let x = amt of reduction in the length and width
:
(8-x)*(6-x) = 24
48 - 8x - 6x + x^2 = 24
:
Arrange as a quadratic equation
x^2 - 14x + 48 - 24 = 0
x^2 - 14x + 24 = 0
:
Factors to
(x-2)(x-12) = 0
:
Two solution but
x = 2 dm reduction is the only reasonable solution
:
new dimensions 6 by 4
Check
(8-2) * (6-2) = 24