I’m Math Dad, and this is Science Mom, ready

for challenge problem number 35. Join us. Give your brain a little exercise, and

see if you can beat me to the answer. Today’s problem is an area maze where you

have to find the missing value. So the figure is made up of rectangles that are

stacked together. They’re not to scale, and each of the numbers represents

either an area or a length. So when you think they’re not to scale I can’t assume

that this is a square. That’s correct. You know the area is 12 and you don’t

even know that they have integer area or integer side lengths. You just know

that the area is 12. Ok, and I need to find out what this length is? Correct. Any

other questions? No. All right. Today you get three separate area mazes to solve,

and I’m giving you five minutes to do it. So those of you watching at home

might want to pause the video each time she comes to a new problem. Your time

Science Mom begins now. All right, so I know this length is 4, and the only way for us

to get an area of 16 would be 4 times 4 so this is 4. Oh and that means that this

length right here is as well because these both have to be equal so that’s 4.

4 times what gives me 24? That would be 6 here. Good. And that means that this whole

entire length is 10 which means that this entire length is 10 as well and now

I mean I could add up all the areas and then try and figure out what that length

is, but that seems not the best way to go about it. How am I going to find this length? So, for 18, I could have three times six

gives me 18. Two times nine but can I assume it can’t be two times nine cuz

that would be way too skinny? It’s not to scale. It’s not to scale, but then I only

have a length of one here, and that would work. We also don’t know that they’d have to be whole

numbers. Oh well I think three and six looks really good here which would get

that four but I feel like I’m kind of cheating, like I’m not getting there with

really… Combine the bottom two boxes… Haha! Now tell me. You’re supposed to add the 12 and

18 is 30 and since the width is 10… okay. So the total area is 30 and then since we

know this is 10 we can, with confidence, not just a guess like I did, say this is 4.

Move to the next problem. Okay. Three minutes. Okay this make the seven this length is

7 we want to know this area 10… 9… Huh, oh I like this one. I feel like this

is kind of sneaky. This has to be 7 times 5 gives me 35, which means if this

whole length is 9 this has to be 4. Good. Um that’s 4. That doesn’t seem to

really help me out very much… Oh that’s 4. That means that this would… oh but

they don’t have to be integers. Can I have just a little tiny bit of a hint?

Well the total height of the question mark box is… Oh total height of that is

10 which means that this is 6 like Six times something that is less than

seven give us 18, but again I don’t want to just assume that this length here is three, but if there’s this would be for you noticing me here yes six times what

is 18 yeah… okay. So that means this length is 4. 4 times

10 is 40. Ha ha. 1 minute. Okay um… dang like I don’t have enough information here. 4

times you get that area so I need to know what this right here is this length

here you’d be nice to kind of assume that 5 times 5 is 25 does this like what

you were doing there you you could extend that line upwards extend that

line up I know this length is 6. oh and I know this length is 4 and it’s

6 times 4 is 24 I know the area of this is 24. 10 seconds… 24!

Explain that one! It’s this thing called luck which I have in abundance. Yeah I mean really

my thought was just like ooh like this box looks to be the same as that box so that was totally

just a lucky guess yep but apparently this really is 24 because, let’s see if

we can reason this out, because um… What’s the area of the upper left corner box? 49

minus 20, which is 25 ,and because these are all

right angles these left two rectangles share the same base width so that means

that the two heights are gonna have to be equal because they have the same area.

Okay. These two here share the same base they’re gonna share

the same area the two on the right. Today I learned area mazes were invented

by Naoki Inaba. Did I say that right? No idea. And if you would like to find

more problems like this just do a search for “area mazes” and you will come up with a

lot. They’re a fun sudoku-like puzzle for your brain to sort of try out

some reasoning.