SOLUTION: Please help me how to solve this problem.Thanks. Ramon wants to fence in a rectangular portion of his back yard against the back of his garage for a vegetable garden. He plans t

Question 1051181: Please help me how to solve this problem.Thanks.
Ramon wants to fence in a rectangular portion of his back yard against the back of his garage for a vegetable garden. He plans to use 68 feet of fence, and needs fence on only three sides. Find the maximum area he can enclose. (Hint: The lengths of the 3 fenced sides of the rectangle must add up to 68.)
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
we know that
:
1) l + 2w = 68, where l is the length and w is the width of the rectangle
:
also
:
2) l * w = Area of the rectangle
:
solve equation 1) for l
:
l = 68 - 2w
:
substitute for l in equation 2)
:
w * (68 - 2w) = Area
:
-2w^2 + 68w = Area
:
The equation for the Area in terms of w is a parabola that opens downward, so
we know that w is maximum at the vertex
:
To find w, we take the first derivative of the equation for Area, then set it
equal to 0 and solve for w
:
-4w + 68 = 0
:
-4w = -68
:
w = 17
:
l = 68 -2(17) = 34
:
*****************************************
Maximum Area is 34 * 17 = 578 square feet
*****************************************
:

RELATED QUESTIONS
Hi I was wondering if someone could help me understand this question. Please and Thank... (answered by stanbon)

Please help me solve this problem: Manuel plans to install a fence around the... (answered by rfer)

James has 66 yards of fencing. Each fence panel is 3/4 yard long. James wants to fence a... (answered by josmiceli)

Sam wants to build a fence in a rectangular space in his back yard. This will be a safe... (answered by wrex)

please help me with this problem ): I have no idea where to begin and how to solve this.... (answered by josgarithmetic,josmiceli)

I am not sure how to go about this word problem so can you please help me solve this... (answered by nerdybill)

Please help show me how to do this word problem: Find the area in square feet of a... (answered by Earlsdon)

Please help me: Ramon is six years older than Mark. In four years, Mark will be as old (answered by jim_thompson5910)

Please help i don't understand this at all! Q: Elin wants to fence two different garden... (answered by ewatrrr)