Suppose you have 54 feet of fencing to enclose a rectangular dog pen. The function a=27x-x^2, where x=width, gives you the area of the dog pen in square feet. What width gives you the maximum area? Round to the nearest tenth as necessary.

Question

amistre64 · Answer

what is the axis of symmetry for your quadratic?

amistre64 · Answer

or if you know the calculus, define the derivative to be zero

anonymous · Answer

This is for algebra, so to be honest, I'm not sure. My friend was looking at this problem, I was intrigued by it, so I tried it out.

amistre64 · Answer

do you know what the shape of the graph would look like?

amistre64 · Answer

there is also a factoring way to approach it;  define the midpoint between the zeros

anonymous · Answer

Well I do know that the answer is supposed to be 
width= 13.5 ft; area=182.3 ft squared

anonymous · Answer

I'm real sorry, I didn't really know much background before asking this question, it's alright if you don't want to solve it

amistre64 · Answer

since this is algebra; lets define the values of x for which it is zero

27x-x^2 = 0

x (27-x) = 0

now, we should know that when we multiply anything by 0 we get 0;  so this tells us that either:

x = 0,  0 (27-0) = 0

or 

x = 27,  27 (27-27) = 0

amistre64 · Answer

a quadratic will have its minimum or maximum value (depending on how it opens) at the middle point between the zeros

halfway between 0 and 27 is:  13.5

anonymous · Answer

Hmmm.... so assuming that similar problems were taught in a school lesson, they would first have to instruct the class that the minimum/maximum is at the middle point between the zeros

amistre64 · Answer

in algebra class, they go over the properties of a quadratic equation;  so this would have been reviewed at some point during the class yes

amistre64 · Answer

some quadratics never touch the x axis, so there are a few ways to approach this;  this was just an easy one to assess by facoting

amistre64 · Answer

*factoring

anonymous · Answer

So then what steps would I use to go about figuring out the maximum area? THANK YOU SO MUCH BY THE WAY

amistre64 · Answer

well, once you know the value for x, plug it in and work the 4th grade math skills ...

anonymous · Answer

Alright, much appreciated, I really have to start easing back into math before school start ;)

amistre64 · Answer

good luck :)

anonymous · Answer

Thanks!