Question

What formula do i use to get the answer?

Answer 1

1. For the right triangular prism below:
A) Find the length of side d.

Answer 2

I dont know what formula i use to find the length?

Answer 3

Well, isn't the end of that a right triangle, where we know the two sides, and need to find the hypotenuse? Do you know any theorems that would help us to do that?

Answer 4

I know how to caculate surface area volume etc.

Answer 5

Which end?

Answer 6

Are you talking about the elngth of c=12

Answer 7

Length*

Answer 8

the end that has side d as part of it

Answer 9

Isnt it the hypotenuse formula

Answer 10

The missing length?

Answer 11

Isnt their a formula so i can find that missing length

Answer 12

Yes. What is the value of d?

Answer 13

I dont know

Answer 14

Use the Pythagorean theorem. Do you remember it?

Answer 15

I do not, can you plz remind me?

Answer 16

In a right triangle with sides \(a\), \(b\) and hypotenuse \(c\), \[a^2+b^2=c^2\]

Answer 17

Ok let me right it on paper

Answer 18

One second.

Answer 19

Ok

Answer 20

Got it written

Answer 21

Do i feel in the variables with the information given?

Answer 22

yes.

Answer 23

Ok i am doing it on paper

Answer 24

One second let me get a tissue real quick i am sick.

Answer 25

I'm not going anywhere

Answer 26

Thank you.

Answer 27

Alright i got it filled in.

Answer 28

So let me do the powers.

Answer 29

Ok i got this 64+36=144

Answer 30

a^2+b^2=c^
8^+6^=12^2
64+36=144

Answer 31

Thats how i got it

Answer 32

You there?

Answer 33

okay, so what is the value of \(d\)?

Answer 34

Uhhh

Answer 35

Since i got 64+36=144 what do i do now?

Answer 36

I get 100=144

Answer 37

Then i kinda stuck right here?

Answer 38

That's the tip-off that your arithmetic needs some work :-)

\[a^2+b^2=c^2\]We know \(a = 8\) and \(b=6\):
\[8^2+6^2 = c^2\]\[64+36 = c^2\]
what is \(64+36=\)?

Answer 39

Ohhh ok but when you look at the picture i gave you it says c equals 12?

Answer 40

Since its a prism

Answer 41

Do i include that or i just concertrate on A,B,D

Answer 42

64+36=10,000

Answer 43

ah, you're being confused by the labeling on that diagram. Ignore it. We are only talking about this triangle, and for our purposes, the hypotenuse is called \(c\)

Answer 44

64+36=10,000?!?

Answer 45

Yeah, cause c^2 power right?

Answer 46

here I always thought 64+36 = 100

Answer 47

I think i got confuse cause the formula said c^2

Answer 48

So 100*100 is 10,000

Answer 49

But if i got 100 so my length would be 100 O:

Answer 50

no. look at what I wrote:

\[a^2+b^2=c^2\]\[8^2+6^2=c^2\]\[64+36=c^2\]\[100=c^2\]\[c=\]

Answer 51

Ohhhh

Answer 52

What happen to the 100?

Answer 53

c=0?

Answer 54

Did you do 100=c^2
- c^2

Answer 55

Im comfused O:

Answer 56

if \[100=c^2\]what does \(c =\) ?

Answer 57

Uhhhhh...

Answer 58

what number \(c\) satisifies \(c*c = 100\)?

Answer 59

10?

Answer 60

Oh ok i get what you did :P

Answer 61

yes!

so the hypotenuse of that triangle with sides a = 8 and b = 6 is length 10. they labeled it "d" in the diagram.

Answer 62

Ok let me explain it to you and tell me if i get it XD

Answer 63

Alright so when we got to the part 100=
c^2

Answer 64

what did you do to get 10 thats what i am comfused about

Answer 65

Did you put a number and see what fit 100 evenly?

Answer 66

Kinda like trial and error

Answer 67

Well, I just know that 10*10 = 100, so I would write down c=10 without thinking. But what I did is take the square root of both sides:
\[c^2= 100\]\[\sqrt{c^2} = \sqrt{100}\]\[c = \sqrt{100} = 10\]

Answer 68

Ahhhhhhhhh

Answer 69

Ok i see now

Answer 70

Good. so that's the first part of the problem, right?

Answer 71

Can you hold on one second let me see if i can do it on paper.

Answer 72

Yeah i did it!

Answer 73

Ok but when you say this is the first part of the problem whats the second part O:

Answer 74

well, the picture asks us to find the base area, does it not?

Answer 75

Well yes it does O:

Answer 76

But before we continue

Answer 77

What is the formula i used called?

Answer 78

the Pythagorean theorem

Answer 79

Ok, Let me take notes

Answer 80

And one more question on this formula

Answer 81

Why didnt i apply 12 to c^2

Answer 82

Is it because if i would write it i would write it as such

a^2+b^2=d^2

Answer 83

Because d is the missing length

Answer 84

yes. the letters are just symbols or placeholders. the Pythagorean theorem still works no matter what letters you use:

<length of 1 side>^2 + <length of 2nd side>^2 = <length of hypotenuse>^2

Answer 85

Ok good, because it was c i thought it wanted me to apply 12 cause it said c

Answer 86

But like you said palce holder

Answer 87

place*

Answer 88

Writing notes.

Answer 89

and when you fliped them what property did you use?

Answer 90

what, you mean when I did\[10 = c\]\[c=10\]? or what?