Solve Algebraic Question: Maximum Garden Area w/ 150ft Fence

[MM92]

Hi everyone, I am new to this site. I was wondering if anyone here can help me answer a question, in order for me to study correctly for my math test tomorrow.

Here's the question:

Melissa plans to put a fence around her rectangular garden. She has 150 feet of fencing material to make the fence. If there is to be a 10 foot opening left for an entrance on one side of the garden, what dimensions should the garden be for maximum area? This question has to be answered in vertex form.

If anyone can answer this and explain it step by step to me that would be great!

 

[mathman]

You should fill in the details by answering the following:
(1)Fence and opening = ?
(2)What shape rectangle is maximum area for given perimeter?
(3)Using (1) and (2), what is length of side.?

 

[kesh]

You should fill in the details by answering the following:
(1)Fence and opening = ?
(2)What shape rectangle is maximum area for given perimeter?
(3)Using (1) and (2), what is length of side.?

but are you allowed to just know what shape of rectangle maximises area? or do you have to show it using calculus

anyway some clues

what is the total perimeter, given the 150 feet of fencing and the 10 feet of gap?

edit: whoops. i mean, ahem, is this number divisible by 4

 

[Gib Z]

Its late and i gtg, so ill post explanation tomoro, but it is, 3 sides are 40, and the side with the 10 gap is 30. getting you 1600 square units.

 

[mathman]

but are you allowed to just know what shape of rectangle maximises area? or do you have to show it using calculus

You don't need calculus. Area of square, side x is x². Rectangle with same perimeter (not square) would have area (x+a)(x-a), which is obviously smaller.

 

[kesh]

You don't need calculus. Area of square, side x is x². Rectangle with same perimeter (not square) would have area (x+a)(x-a), which is obviously smaller.

oh yeah, duh. you get used to general methods and forget the obv