Justin wanted to plant a rectangular vegetable garden. He bought 60 ft of fencing to enclose his garden. Justin wants to enclose the maximum area for his garden. What dimensions should Justin use for his vegetable garden?

Question

anonymous · Answer

@Hero No... this is part of 8th grade algebra Lol I'm REALLY confused

hero · Answer

This is the kind of problem where I believe you're supposed to use 2 formulas

$A = xy$
$P = 2x + 2y$

hero · Answer

A = area of rectangle
P = perimeter of rectangle

hero · Answer

We know what the perimeter is, therefore:

$60 = 2x + 2y$

hero · Answer

If I'm not mistaken, the only way the area can be maximum is if it is a square. So in other words x must equal y in order for this to work.

hero · Answer

So in reality when you replace y with x, you end up with these two equations:

$A = x^2$
$60 = 4x$

hero · Answer

Now, you solve for x in the second equation to get

$x = \frac{60}{4}$

hero · Answer

Of course $\frac{60}{4} = 15$ so we substitute x = 15 into the Area formula to get:

$A = 15^2$

hero · Answer

So now all you have to do is calculate $15^2$. Don't forget units will be $\text{ft}^2$

anonymous · Answer

@Hero Thank You SOOOOO MUCH!!!! :)

hero · Answer

I'm just curious to know what other way (other than calculus) that you're supposed to use to solve this. You probably didn't know that a square area of the same perimeter will have maximum area compared to a rectangle of the same perimeter. That's not really an algebraic rule.

hero · Answer

If you can explicitly state what the correct answer is, I'll give you a medal.

hero · Answer

Btw, I'm not a 10 year old kid.

anonymous · Answer

@Hero First of all, if I knew how to solve this, would I have asked the question in the first place? Second of all, no one said you were a 10 year old kid. And third of all, I could really care less if I got a medal or not

hero · Answer

lol, okay