Question

Find the value of OU and RC if triangle YOU ~ triangle RCK.

Answer:


RC = 4, OU = 20

RC = 12, OU = 60

RC = 60, OU = 12


RC = 20, OU = 4

Answer 1

You basically got: two similar (i.e. proportional) Pythagorean triples.

Answer 2

Can you tell me the side CR please? (use: \(\large\color{slate}{a^2+b^2=c^2 }\) )

Answer 3

ok but which numbers do i square ?

Answer 4

you have a side 3 and 5. 5 is c, (since it is the hypotenuse)
your unknown is the b.

\(\large\color{slate}{3^2+b^2=5^2 }\). (then solve for b, but include positive answer only)

Answer 5

9 + b^2 = 25
b^2 = 25 - 9
b^2 = 16

Answer 6

yes, then \(\large\color{slate}{b=? }\)

Answer 7

square root both sides, (but without the \(\large\color{slate}{\pm }\) next to the root)

Answer 8

b = 4?

Answer 9

yes

Answer 10

and OU is equal to?

Answer 11

\[\sqrt{16} = 4\]

Answer 12

ok so RC = 4 now we need OU

Answer 13

yes, we need OU

Answer 14

\[16^2 + b^2 = 12^2\]

Answer 15

OU is the hypotenuse, incorrect setup

Answer 16

you don't need that

Answer 17

I will show you a couple of sets of Pythagorean triples that are multiples of each other as a hint.

Answer 18

\(\large\color{slate}{ 3^2+4^2=5^2 }\)

\(\large\color{slate}{ 6^2+8^2=10^2 }\)

\(\large\color{slate}{ 9^2+12^2=15^2 }\)

\(\large\color{slate}{ 12^2+16^2=\color{red}{?}^2 }\)

Answer 19

256 + b^2 = 144
b^2 = -112

Answer 20

you always set the hypotenuse as c, when you have:
\(\large\color{slate}{ a^2+b^2=c^2 }\)

Answer 21

Look at my post though, see what I am trying to show?

Answer 22

yea i just noticed, im getting confused on this one

Answer 23

just show me how to get OU

Answer 24

these are just proportional Pythagorean triples. I am showing how all of the aforementioned sets (including the one with the red question mark) ARE, multiples of the first set, (i.e of \(\large\color{slate}{ 3^2+4^2=5^2 }\) ).

Answer 25

I am showing the quick way. If you want to go through plugging into \(\large\color{slate}{ a^2+b^2=c^2 }\) , then:

Answer 26

\(\large\color{slate}{ 12^2+16^2=c^2 }\) (hypotenuse is unknown)

Answer 27

then solve for c.

Answer 28

400

Answer 29

160000

Answer 30

when you simplify the left side, you get 400. So you have this: \(\large\color{teal}{ 400=c^2 }\)

Answer 31

Now, you need to square root both sides, not to raise both sides to the second power.

Answer 32

ok so it would be 20

Answer 33

yes

Answer 34

ok thanks

Answer 35

yw