C2 - Applications of Differentiation

Q:This diagram represents the end view of the outer cover of a match box, AB and EF being gummed together, and assumed to be the same length.

If the total length of edge (ABCDEF) is 12 cm, calculate the lengths of AB and BC which will give the maximum possible cross-section area.

So, I'm struggling a lot on this question. Help would really be appreciated.

...

Dramatic much?

Don't hate because I make maths fun.

HA! I got you! $A=xy$, yes. But we also know that $x+y = 6 \Rightarrow y = 6-x$, so really, we can just write $A = xy = x(6-x) = 6x - x^2$. HALLELUJAH, IT'S ALL IN ONE VARIABLE IN X and it's an easy quadratic! Why'd I cry? Things are good in life again.

So, what'd $\frac{\mathrm{d}A}{\mathrm{d}x}$? What value of $x$ makes it zero? What's the corresponding value of $y$? (hint: $y = 6-x$, don't tell the maths fairy I told you that! )

"Fun", yeah...

are you on drugs? this made me laugh a lot

are you on drugs? this made me laugh a lot

Drugs are not cool, kids.

you've gone from "full solutions are against forum guidelines" to this

you've gone from "full solutions are against forum guidelines" to this

HA! I got you! $A=xy$, yes. But we also know that $x+y = 6 \Rightarrow y = 6-x$, so really, we can just write $A = xy = x(6-x) = 6x - x^2$. HALLELUJAH, IT'S ALL IN ONE VARIABLE IN X and it's an easy quadratic! Why'd I cry? Things are good in life again.

So, what'd $\frac{\mathrm{d}A}{\mathrm{d}x}$? What value of $x$ makes it zero? What's the corresponding value of $y$? (hint: $y = 6-x$, don't tell the maths fairy I told you that! )

i'm not a ****ing wizard hagrid im just zacken

EDIT: why did TSR take my all caps away

what a video that was, back in the day, I think ill actually go watch it again, someone should do a zacken edit

Drugs are not cool, kids.