SOLUTION: the sum of the length I and the width w of a rectangular region is 190 meters Find the dimensions that produce the greatest area

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Question 976849: the sum of the length I and the width w of a rectangular region is 190 meters Find the dimensions that produce the greatest area
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
L%2BW=190
.
.
A=L%2AW
From above,
L=190-W
A=%28190-W%29W
A=190W-W%5E2
To find the maximum value of a quadratic, convert to vertex form,
A=-%28W%5E2-190W%29
A=-%28W%5E2-190W%2B9025%29%2B9025
A=-%28W-95%29%5E2%2B9025
So the maximum area 9025m%5E2 occurs when W=95m so then
L=190-95
L=95m