Have I done this right? (area using Differentiation)

[Farvahar021]

hey,
well the question is work out the largest area of a rectangle when the perimeter is 160.
this is how i done it...
image: http://imageshack.us/photo/my-images/685/mathm3.jpg/

this is where i get confused.... is 40 the area?? or is it just y length in the rectangle, if so then x must be 40 too if you put it back into the perimeter equation which makes it a square not a rectangle.

thanks

 

[mmm4444bot]

is 40 the area? Nope


or is it just [one dimension of] the rectangle Of course it is!

After all, YOU defined the meaning of symbol y yourself. (Look at your diagram.)


if so then x must be 40 too Yup


if you put it back into the perimeter equation Um, it would be easier to use YOUR formula for x:

I mean, instead of going back to the perimeter equation, substitute y = 40 into x = 80 - y


which makes it a square not a rectangle Oops! All squares ARE rectangles.

Let this exercise be a "lesson" for you because you'll probably come across similar scenarios in the future.

The largest area of any rectangle constrained by some given perimeter is when that rectangle is a square.

Cheers ~ Mark

 

[Farvahar021]

I swear if only our maths teacher was like you...

thanks!

 

[mmm4444bot]

I don't want you swearing, but thanks nonetheless.

Did you ever find out exactly what your teacher expected on that "linearizing with logs" exericse? I seem to remember that it maybe contained some typographical errors.

 

[Farvahar021]

Yeah you were right it was a typo, it asked for I by mistake instead of i

thanks again