SOLUTION: Id need help here please, find the dimensions of a rectangle "a" with the greatest area whose perimeter is 30feet. I know that the perimeter of a rectangle is 2l+2w=P and i also kn

Question 204292: Id need help here please, find the dimensions of a rectangle "a" with the greatest area whose perimeter is 30feet. I know that the perimeter of a rectangle is 2l+2w=P and i also know that to solve for the length; l= p-2w/2 and to solve for the Area; A=lw but here i dont have the length or width so how would I solve this problem?? I have came as far as; l=p-2w/2 so l=30(ft)-2w/2... I now i didnt come far and that its pretty lousy -_- that i only came as far as that, but thats exactly why i need help.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the perimeter formula

Plug in (the given perimeter)

Factor out the GCF 2

Divide both sides by 2

Subtract W from both sides

Rearrange the equation

---------------------------

Move onto the area of a rectangle formula

Plug in

Rearrange the terms.

Now the goal is to maximize "A". You can think of "A" as a function of "W". In other words, the area "A" is dependent on "W". There are a number of ways to maximize "A", but the easiest way is to graph to get

From the graph, we can see that the max area of occurs when the width is (note: use the trace/extrema feature on your calculator).

Now simply divide the area by the width to get the length

============================================================

Answer:

So the max area or 56.25 square feet occurs when the dimensions are 7.5 feet by 7.5 feet.

Note: this is important to notice that the max area occurs when the figure is a square. So for any given fixed perimeter of a rectangle, the max area will result from a square. This may come in handy when you're trying to get the most out of your yard (in terms of area) and keep the cost of fencing to a minimum.

RELATED QUESTIONS
Find the dimensions of a rectangle (a) with the greatest area whose perimeter is 30... (answered by Alan3354)

can someone help me,i dont get this!!! Find the dimensions of a rectangle a with the... (answered by mathispowerful,scott8148)

please help me with this question i dont understand it at all. find the dimensions of a... (answered by josmiceli)

Can you help with this problem? Find the dimensions of a rectangle "a" with the... (answered by funmath)

find the dimensions of a rectangle "a" with the greatest area whose perimetter is 30... (answered by stanbon,solver91311)

find the dimentions of a rectangle( a )with the greatest area whose perimeter is 30... (answered by venugopalramana)

Find the demensions of a rectangle a with the greatest area whose perimeter is 30... (answered by checkley77)

Find the demensions of rectangle A with the greatest area whose perimeter is 30... (answered by Mathtut)

Find the dimensions of the rectangle of greatest area whose perimeter is 20... (answered by drk)