SOLUTION: Mr. Hanson wants to enclose a rectangular portion of his yard for his dog Gigi. He has 200 feet of fencing. He wants to maximize the amount of area. Sketch and label the sides of

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Mr. Hanson wants to enclose a rectangular portion of his yard for his dog Gigi. He has 200 feet of fencing. He wants to maximize the amount of area. Sketch and label the sides of       Log On


   

Question 926521: Mr. Hanson wants to enclose a rectangular portion of his yard for his dog Gigi. He has 200 feet of fencing. He wants to maximize the amount of area.
Sketch and label the sides of the rectangle with variables.
Write and maximize a quadratic function for the AREA of his barking lot.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the length of a side
The length of the other side is +%28+200+-+2s+%29+%2F+2++=+100+-+s+
The area is:
+A+=+s%2A%28+100+-+s+%29+
+A+=+-s%5E2+%2B+100s+
The maximum is at:
+s%5Bmax%5D+=+-b%2F%282a%29+
+a+=+-1+
+b+=+100+
+-b%2F%282a%29+=+-100+%2F+%28+-2%29+
+-b%2F%282a%29+=+50+
+s%5Bmax%5D+=+50+
-----------------
+4%2A50+=+200+, so the yard must be a perfect square.
The maximum area is:
+A%5Bmax%5D+=+50%5E2+
+A%5Bmax%5D+=+2500+
-------------------
You can check this by making +s+=+49+, find +A+
then make +s+=+51+ find +A+ ( very good check )