SOLUTION: what are the dimensions of a rectangular room that has a perimeter of 48 m and a area of 128 m2

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Question 860476: what are the dimensions of a rectangular room that has a perimeter of 48 m and a area of 128 m2
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If the room measures x meters by y meters,
its perimeter (in meters) would be
2%28x%2By%29=48 ,
and its surface area (in square meters) would be
x%2Ay=128 .

2%28x%2By%29=48 <---> x%2By=48%2F2 <---> x%2By=24
Since 128=2%5E7=16%2A8 and 16%2B8=24 ,
it is obvious that the room could be highlight%2816%29 meters long by highlight%288%29 meters wide.

The teacher may expect that you solve x%2By=24 for y ,
x%2By=24 <---> y=24-x ,
and then substitute into x%2Ay=128 ,
to get a quadratic equation:
x%2A%2824-x%29=128 --> 24x-x%5E2=128 --> x%5E2-24x%2B128=0
You can solve x%5E2-24x%2B128=0 to get the two solutions
x=8-->y=24-8=16 ,
and
x=16-->y=24-16=8 ,
which tell you that the dimensions of that rectangular room
are highlight%2816%29 meters (length) and highlight%288%29 meters (width).