u/socratictutoring

You'll be revisiting this problem later on in AP Calculus, under related rates.

But we can solve this problem without any advanced mathematical machinery! Think: as the side length increases by 1 unit, how does the perimeter change? How does the area change?

For the perimeter, this is easy - it increases by 4 units if the sidelength is increased by 1 unit. What about the area?

You may have realized that the rate at which the area increases depends on the current sidelength! If we have sidelength s, then increasing by 1 takes our area from s^(2) to (s+1)^(2). So the increase in area is 2s + 1.

Thus, while the square is small, our perimeter grows faster, but as the square increases in size, the area grows faster. The transition happens around when 2s + 1 = 4, or when our sidelength is 2.

Hi Everyone! I'm Esther, a Cambridge-based math and physics tutor. I'm an MIT physics graduate with 10+ years of tutoring and teaching experience, and I work with high school and college students both locally (including in Concord) and online.

I specialize in AP Calculus AB/BC, AP Physics C, and college-level math and physics (including probability/statistics, differential equations, linear algebra). If you or your student could use support this school year, feel free to dm me or check out socratictutoring.com .

Congrats on wrapping up Mechanics today! For those of you taking E&M, feel free to ask any content questions below :)

You've got this!

Hi all, I'm Esther - I've been tutoring AP Calculus for the past decade. With the exam only 5 days away, bring your questions here! Questions on unit 10 are especially encouraged :)

Hi all, I'm Esther - I've been tutoring AP Physics C for the past decade. I'll be answering questions in this thread over the next few days, so hit me with any problems you've been struggling with in either Mechanics or E&M.

I'm happy to answer any questions related to Physics C, but the best ones are concrete questions about content, so I'll be prioritizing those.