Hii

[Artemisss]

Ian has 280 meters of fencing to enclose a rectangular land that borders on a wall of a building.If he doesnt fence the side along the wall,what is the largest area that can be enclosed?

 

[Steven G]

What have you tried? Where are you stuck? If you had read the posting guidelines you would have known that you need to share your work so the tutors here know what type of help you need.

Please read the posting guidelines and post back following those rules.

 

[Dr.Peterson]

Ian has 280 meters of fencing to enclose a rectangular land that borders on a wall of a building.If he doesnt fence the side along the wall,what is the largest area that can be enclosed?

Can you write an expression for the area as a function of the length along the wall? Please show whatever work you can do, so we can know where you need help.

 

[HallsofIvy]

Let x be the length of the side parallel to the wall. Since there are 280 m of fencing available, that leaves 280- x for the other two sides so each side is (280- x)/2= 140- x/2 m. The area is \(\displaystyle x(140- x/2)= 140x- x^2/2\).
You can "complete the square" to write that as \(\displaystyle (1/2)(A- (x-x_0)^2)\). Since a square is never negative, that is A/2 minus something. This will have maximum value, A, when \(\displaystyle x= x_0\).