Can't understand how to solve this, please help

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[fading sage]

What have you tried to begin with?

You shouldn't think in terms of formulae.

You should think in terms of geometry.

Like, actually picture the shape in your head. What's the perimeter?

And I mean, like, at the most basic level.

What do we mean when we talk about the perimeter of a shape?

What do you mean "total length"?

Okay.

So we have a rectangle with a semicircle attached to it.

Notice, what don't we have in this picture?

What would we have if the rectangle and semicircle were separate that we don't have when they're together?

We would have another side on each shape. Which side would that be for the rectangle?

...okay, that's what it is for the semicircle. What is it for the rectangle?

Right. Also, notice that the sides we're losing must have the same length, or else we'd have overhang on one side or the other of the join. So what does this mean for the rectangle?

Because what's the definition of a rectangle?

So a kite is a rectangle?

And...?

What else can we say about rectangles?

Therefore, in this rectangle...?

Which is what?

Yes.

Explain.

Explain each term.

Right, and what does w equal?

...no, what does w equal?

I mean, not necessarily.

...what did we just say w was equal to?

So?

So the perimeter?

[twin mortar]

You are on the right track

[fading sage]

...no.

You made a mistake.

Starting with 2l + (2 + pi)r = 40, go one step at a time to tell me what l equals.

Not quite.

l = (40 - (2 + pi)r)/2. You were missing the parentheses grouping the numerator together.

Because of the order of operations, remember.

You could also say l = 20 - (2 + pi)r/2, without worrying about grouping, because of how division and multiplication work.

Apart from grouping the two coefficients of r together, which I do mostly because I think it's more convenient.

If you didn't feel like doing that, you would get l = 20 - r - pi r/2.

Anyway. Whichever form you choose for the relation between l and r, the important part is that we have it, and so now we can describe anything about this shape purely in terms of r.

So now we turn our attention to area.

What's your area formula?

Again, explain each term.

Right. To be clear, I'm not necessarily disagreeing with you when I ask you to explain a formula, it's just that the most important part of knowing a formula is knowing what it means.

Because if you know what it means, you can modify it or manipulate it to apply it to different circumstances. It's not just a black box where numbers go in and answers come out.

Sure.

Also, I noticed a typo here.

[fading sage]

It's against the rules to hijack someone else's thread. Go make your own.

Observe the middle term.

[urban vale]

ok

[fading sage]

Yes.

It's cubed.

That would give us a volume, not an area.

I mean, I'm interested in how they failed to catch this mistake and somehow managed to work it into the correct answer, probably by making a different mistake that cancelled it out.

See, they didn't make the mistake I'm pointing out.

[random oak]

@zenith verge has given 1 rep to @fading sage

[fading sage]

No problem.