Help!

[briez22]

I'm having a difficult time trying to figure this out . . . where do I begin?

Claire wants to fence in a rectangular plot of land along a wall to make a garden. She has p feet of fencing, which will extend along three sides of the garden, with the wall forming the fourth side. Which of the following expressions in p is equal to the maximum possible area, in square feet of Claire's garden.
The choices are A) 2p^2, B) p^2/2, C) p^2/4 or D) p^2/8. The answer is D and I don't have any idea how they got it . . . Thank you!

 

[burakaltr]

I'm having a difficult time trying to figure this out . . . where do I begin?

Claire wants to fence in a rectangular plot of land along a wall to make a garden. She has p feet of fencing, which will extend along three sides of the garden, with the wall forming the fourth side. Which of the following expressions in p is equal to the maximum possible area, in square feet of Claire's garden.
The choices are A) 2p^2, B) p^2/2, C) p^2/4 or D) p^2/8. The answer is D and I don't have any idea how they got it . . . Thank you!

x(p-2x)=A
xp-2x**2=A
A'=0=p-4x=0
p=4x

so holding p a constant and doing relevant substitutions ie: x inm terms of p

Amax=(p/4)(p-p/2)=(p/4)*p/2

= (p**2)/8

 

[burakaltr]

I'm having a difficult time trying to figure this out . . . where do I begin?

Claire wants to fence in a rectangular plot of land along a wall to make a garden. She has p feet of fencing, which will extend along three sides of the garden, with the wall forming the fourth side. Which of the following expressions in p is equal to the maximum possible area, in square feet of Claire's garden.
The choices are A) 2p^2, B) p^2/2, C) p^2/4 or D) p^2/8. The answer is D and I don't have any idea how they got it . . . Thank you!

OR at

x=p/4

Good Luck !

 

[briez22]

Thank you very much!!

 

[burakaltr]

Thank you very much!!

You are Quite Welcome

I think in this type of assignments , it is crucial to understand which values to hold constant and which to treat like a variable.

All the Best !