Question

Pythagorean Theorem Help

Answer 1

well i took a test about the Pythagorean Theorem and my teacher never teached us about the Pythagorean Theorem and i just need help on this

Answer 2

\[a^2+b^2=c^2\] is the theorem. It's used to find the diagonal of the gright triangle.


a and b are the legs of the triangle, b is the hypotenuse.

Answer 3

I meant right triangle not gright, sorry.

Answer 4

https://app128.studyisland.com/cfw/stylesheets/images/practiceSession/test-interface-sprite.png

Answer 5

So FOR EXAMPLE:

use the theorem, plug in numbers.\[6^2+8^2=c^2\]Solve for c.\[36+64=c^2\]\[100=c^2~~~~~~~->~~~~~c=10\]

Answer 6

oops
If X = 3 units and Y = 12 units, what is the length of Z?

Answer 7

thats the triangle

Answer 8

\[\sqrt{15} \sqrt{153} \sqrt{163}\] 153

Answer 9

\[3^3+12^2=Z^2\]

Answer 10

\[Z=?\]

Answer 11

yes

Answer 12

No, Z doesn't equal "yes", it equals a number, which you should calculate :-)

\[3^2=3*3=\]\[9^2=9*9=\]Add those two numbers together, what do you get?

Answer 13

3x3=9 and 9x9=81

Answer 14

sorry 9+9=18 and 3+3= 6

Answer 15

sorry, that should have been \[12^2 = 12*12 = \]no idea where 9 came from!

Answer 16

LoL

Answer 17

12-3=9, that must be it :-)

Answer 18

12-3=9 yes its correct

Answer 19

but back to the real problem, what is \[12^2= 12*12 =\]

Answer 20

so is it 12+12 or 12x12

Answer 21

\(12*12\) is multiplication

Answer 22

ok 12x12=144

Answer 23

right, so by Pythagorean theorem, \[Z^2 = X^2+Y^2\]and we have determined that \[X^2=3*3=9\]and\[Y^2=12*12=144\]

Answer 24

what does \(Z^2=\)
what about \(Z=\) (which is what the problem requests we find)

Answer 25

hmm z must be 144 but i might be rong

Answer 26

No, \[Z^2 = X^2+Y^2 = 9+144 = \]

Answer 27

153

Answer 28

Right. So if \[Z^2=153\]what does \[Z=\]

Answer 29

153 or

Answer 30

am i rong?

Answer 31

Well, if Z*Z = 153, can Z=153?

Answer 32

I haven't made a close study of the number 153, but I think the answer is no :-)

Answer 33

so we might have to divide

Answer 34

we need the square root of 153, or \(\sqrt{153}\)
the square root of some number is defined as another number, which when multiplied by itself, gives you the first number. For example, the square root of 4 is 2, because 2*2 = 4.

Answer 35

\[\sqrt{x}*\sqrt{x} = x\]
\[\sqrt{153}*\sqrt{153} = 153\]
So if \[Z^2=153\]then \[Z=\sqrt{153}\]

Answer 36

ok so thats the answer Z\[\sqrt{153}\]

Answer 37

notice that there was a "trap" answer of 153 in your answer choices, put there to catch careless students who just added X^2 and Y^2 and forgot that that gives them Z^2, not Z

Answer 38

and \[\sqrt{15}\]was probably intended to catch people who forgot to square X and Y before adding them...

Answer 39

there fore thats not the answer?

Answer 40

the correct answer is the one we found: \[Z = \sqrt{153}\]

Answer 41

ok so it was but you where giving me a explanation of the answer right?

Answer 42

2 of the other answers are answers you get if you make various predictable mistakes. I'm not sure how you might get \[Z = \sqrt{163}\]but I'm sure there's some student who could manage to do it :-)

Yes, I wanted you to see the importance of working carefully and not just grabbing the first answer that appears to have a number you got...

Answer 43

right right and i live teachers like you :) how many can you do?

Answer 44

let's do another one!

Answer 45

:D ok

Answer 46

If X = 10 cm and Y = 10 cm, what is the length of Z?