 # Math Dad vs Science Mom 35: Area Maze

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!I’m gonna explain.
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.