SOLUTION: What are the dimensions of the largest rectangular area you can fence with 150 feet of fencing, if you can use the side of your house for one side? side of house dimension is

Algebra ->  Surface-area -> SOLUTION: What are the dimensions of the largest rectangular area you can fence with 150 feet of fencing, if you can use the side of your house for one side? side of house dimension is       Log On


   

Question 700118: What are the dimensions of the largest rectangular area you can fence with 150 feet of fencing, if you can use the side of your house for one side?

side of house dimension is not known
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the length in feet of the
side parallel to the house.
The length of each of the other 2 sides is +%28150+-+x+%29+%2F+2+
The area is:
+A+=+x%2A%28+150+-+x+%29+%2F+2+
+A+=+75x+-+%281%2F2%29%2Ax%5E2+
The general form is:
+A+=+b%2Ax+%2B+a%2Ax%5E2+ where
+a+=+-1%2F2+
+b+=+75+
------------
The x-co-ordinate of the vertex is at
+-b%2F%282a%29+
+-b%2F%282a%29+=+-75+%2F+%28+2%2A%28-1%2F2%29%29+
+-b%2F%282a%29+=+75+%2F+1+
+x+=+75+
+%28+150+-+x+%29+%2F+2+=+%28+150+-+75+%29+%2F+2+
+%28+150+-+x+%29+%2F+2+=+75%2F2+
So, the 3 sides are +75+, +75%2F2+, and +75%2F2+
The maximum area is:
+A+=+75%2A%28+75%2F2+%29+
+A+=+2812.5+ ft2
-------------------
Here's the plot of the area equation:
+graph%28+400%2C+400%2C+-20%2C+160%2C+-300%2C+3200%2C+-%281%2F2%29%2Ax%5E2+%2B+75x+%29+