Question

Find the missing lengths of the sides.

Answer 1

where?

Answer 2

Alright. Are you familiar with the notation with the small dashed lines?

Answer 3

yes.

Answer 4

Like A = 6 there

Answer 5

yes

Answer 6

ok then nvm lol

Answer 7

Oh okay then. So we know that whatever the answer will be, a and b will be the same. So we can immediately rule out b).

Answer 8

XD, Tanks tho .fedorable.

Answer 9

ok

Answer 10

Now, question, have you ever seen something called the "Pythagorean Theorem?"

Answer 11

yes, a^2 + b^2 = c^2

Answer 12

Alright then. So do we know any of the values in that equation right now?

Answer 13

Yes, I know that c = 12 sqrt(2)

Answer 14

Awesome. Now, we know that a = b right?

Answer 15

right

Answer 16

So whenever we have an equals sign, we can substitute one for the other right?

Like if x=y then if x=5 then y=5 right?

Answer 17

the easier way to do is just do 12sqrt(2)/sqrt(2), becuase we know its a 45/45/90, which means the legs are 1/sqrt(2) of the longest side

Answer 18

right @ Hitaro

Answer 19

So we can make this equation

a^2 + b^2 = c^2
a^2 + b^2 = (12sqrt( 2 )) ^2
a^2 + a^2 = (12sqrt (2 )) ^2

Answer 20

ok. That makes sense.

Answer 21

So is there any way we can simplify that?

Answer 22

yes, u can add like variables.

Answer 23

Right. So that would be 2a^2 = 12(sqrt2)^2

Answer 24

Think you can take it from there?

Answer 25

\[2a^2 = (12\sqrt{2})^2\]

Answer 26

I would have to get a by itself right...

So, 2a^2 = 12(sqrt)2^2
2a^2 / 2 = 12(sqrt)2^2 / 2
a^2 = 6(sqrt)2...

No, I don't get it... Im sorry. Could u pls walk me thru it.

Answer 27

I wrote the equation wrong in text form, that's my bad. the 12 is inside the square.

Answer 28

The correct equation is a couple replies up.

Answer 29

Oh! I see it Tanks. Let me try again.

Answer 30

2a^2 = (12sqrt2)^2
here is where i am confused, am I supposed to get rid of the square first or the 2 before the a, to get a^2 by itself?

Answer 31

Right. Right now its a bit difficult to simplify the left side because dividing by two doesn't work. So maybe we can simplify the right side.

Can you simplify (12sqrt(2))^2 ?

Answer 32

12sqrt(2) = 16.9 or 17.

Answer 33

Okay hold on.

Can you solve (sqrt(2))^2 ?

Answer 34

2

Answer 35

Alright awesome. How would you solve (2sqrt(2))^2?

Answer 36

Sorry I am having a lot of lag on my end.

Answer 37

Yeah. Openstudy can be finicky.

So, how might we go about solving (2sqrt(2))^2 ?

Answer 38

Do u mean (12sqrt(2)^2?

Answer 39

Yes.

Answer 40

(my bad)

Answer 41

k, 24.

Answer 42

Can you walk me through your steps to get that?

Answer 43

I used the calculator. :( I am allowed to do that in my school. Unfortunatly I don't know how to get it.

Answer 44

\[2a^2 = (12\sqrt{2})^2\]

Answer 45

Okay. So, let's think this through. Squaring a number is multiplying it by itself.

So we're trying to find 12sqrt(2) times 12sqrt(2)

Answer 46

But this is kinda awkward, because we don't have an intution on how to multiply these quite yet.

So what I'm going to do, is ask you to subtitute z= sqrt(2).

Can you solve 12z times 12z?

Answer 47

144z

Answer 48

Hmm okay.

Can you solve 3a times 3a ?

Answer 49

9a^2

Answer 50

Perfect. So what is 12z times 12z again?

Answer 51

144z^2

Answer 52

Awesome. Now, we substituted z for sqrt(2) right?

so if z = sqrt(2) what is 144(z^2)?

Answer 53

I think it is 144((sqrt(2)^2)

Answer 54

Right, so that's 144(2) right?

So 2a^2 = 144(2)

Answer 55

oh, right

Answer 56

So can you solve for a?

Answer 57

Divide both sides by 2.

Answer 58

?

Answer 59

Right

Answer 60

So, you good? Have you found a?

Answer 61

Ok, so I would end up with a^2 = 144. Then I would end up w/ 12? Right!!

Answer 62

Yep! Awesome job. Hopefully all that muddying around with how to multiply square roots didn't take away from the concept.

Could you solve this simpler problem?

Answer 63

The legs each = 16, right?

Answer 64

well let's remember the steps. What would the pythagorean theorem look like in this situation?

Answer 65

oh, right sorry. 256

Answer 66

Um one sec, a^2 + b^2 = 32^2 or 256

Answer 67

I'm realizing this problem isn't actually easier, I tried to set up one with simple numbers but I think I just made it more complicated.

Answer 68

Im sorry... I thought I was starting to understand.

Answer 69

Either way, you let a =b because the two sides are congruent.

so you end up with a^2 +a^2 = 256
2a^2 =256
a^2 = 128
a = sqrt(128)

Answer 70

No no no, what you said was perfectly right

Answer 71

oh! Ok great!!

Answer 72

Like, imagine I was trying to explain division, so I tried to pick and example like 8 divided by 2
But by accident I actually did 1596/1405

Answer 73

Anyways, does each step make sense? feel free to let me know if it doesn't.

Answer 74

Yes! Thank you so much!! You should be a qualified helper!!

Answer 75

Awesome, feel free to let me know if you have any more questions.