SOLUTION: Find the length and width of a rectangle that has area 55 square centimeters and a minimum perimeter. Round your answer to one decimal place.

Algebra ->  Rectangles -> SOLUTION: Find the length and width of a rectangle that has area 55 square centimeters and a minimum perimeter. Round your answer to one decimal place.       Log On


   

Question 628653: Find the length and width of a rectangle that has area 55 square centimeters and a minimum perimeter. Round your answer to one decimal place.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+A+=+L%2AW+
+55+=+L%2AW+
+W+=+55%2FL+
------------
The formula for perimeter is
+P+=+2W+%2B+2L+
By substitution:
+P+=+2%2A%28+55%2FL+%29+%2B+2L+
+P+=+110%2FL+%2B+2L+
Here's the plot:
+graph%28+400%2C+400%2C+-2%2C+16%2C+-5%2C+50%2C+110%2Fx+%2B+2x+%29+
The minimum perimeter is around +P+=+30+
and +L+=+7.5+
Since ++sqrt%2855%29+=+7.416+., and +4%2A7.416+=+29.665+,
It looks like the perimeter is minimum when the
rectangle is a square.
+P%5Bmin%5D+=+29.7+
OK