SOLUTION: A rectangle has a perimeter of 600 in. Express the area, A, of the rectangle as a function of the length of one of its sides x.

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A rectangle has a perimeter of 600 in. Express the area, A, of the rectangle as a function of the length of one of its sides x.       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 503181: A rectangle has a perimeter of 600 in. Express the area, A, of the rectangle as a function of the length of one of its sides x.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If one side is x, the opposite side is also x
Their sum is 2x
Call the other 2 sides y
Call the perimeter P
+P+=+2x+%2B+2y+
solve for y
+2y+=+P+-+2x+
+y+=+%28P%2F2%29+-+x+
And, since +P+=+600+,
+y+=+300+-+x+
The area os the rectangle is +A+=+x%2Ay+
+A+=+x%2A%28+300+-+x+%29+
+A+=+300x+-+x%5E2+
Here's a plot of area and x:
+graph%28+400%2C+400%2C+-40%2C+330%2C+-1000%2C+25000+%2C+300x+-+x%5E2%29+