Question

I WILL FAN,MEDAL,& TESTIMONIAL

-Find e, if a=8, d=22, b=4
-Find d, if b=6, e=15, a=8
-Find a, if f=32, c=12, d=24
-Find c, if f=15, b=7, e=3
-Find f, if c=2 1/2, d=24, a=10
-Find b, if c=5, e=7, f=9
-Find a, if b=11, e=8, d=6

Answer 1

i bet we are missing something

Answer 2

an expression involving e i hope,

Answer 3

@satellite73 there are triangles, but i cant send a picture its a weird file, i can send you the actual thing ?

Answer 4

by all means post something

Answer 5

@satellite73 there

Answer 6

oh wow
ok it is mostly solving ratios

Answer 7

yeah pretty much, all I have solved is the two riddle up top

Answer 8

which ones have you done? i don't want to repeat any

Answer 9

ive only done the riddles up top

Answer 10

ok lets do the first one

Answer 11

damn i labelled them all wrong

Answer 12

yeah I was confused lol

Answer 13

\[\frac{e}{22}=\frac{4}{8}\] that's better

Answer 14

which really just means \(\frac{e}{22}=\frac{1}{2}\) i.e. \(e\) is half of \(22\)

Answer 15

i feel so dumb right now

Answer 16

did you understand what i wrote?

Answer 17

not really

Answer 18

we can go slower if you like

Answer 19

yes, that'd be helpful ((:

Answer 20

ok we have two triangles that are similar
that means
a) all the angles are the same and
b) the ratios of the corresponding sides are the same
you can forget about the angles for this one
just know that the ratios of the sides are the same
let me draw the picture correctly this time

Answer 21

okay

Answer 22

so for example \[\frac{a}{b}=\frac{d}{e}\] do you see how i got that ?

Answer 23

i think so

Answer 24

right side over the bottom on the left, right sides over the bottom on the right

Answer 25

lets write another one \[\frac{b}{c}=\frac{e}{f}\]

Answer 26

okay I get how you got that

Answer 27

bottom over left on the right, bottom over left on the left
get the idea?

Answer 28

yes

Answer 29

there are more we can write

Answer 30

okay

Answer 31

\[\frac{c}{a}=\frac{f}{d}\] for example

Answer 32

so for the first one, would e=4 ?

Answer 33

and so on and so one because we can flip any of these \[\frac{c}{a}=\frac{f}{d}\iff \frac{a}{c}=\frac{d}{f}\]

Answer 34

lets make a ratio that includes \(a, d, b, e\) because we know three out of those four numbers

Answer 35

okay

Answer 36

\[\frac{b}{a}=\frac{e}{d}\] do you see that one?

Answer 37

yes

Answer 38

now lets plug in the numbers we know for \(a,b,d\)

Answer 39

\[\frac{4}{8}=\frac{e}{22}\] uses

Answer 40

you see what i did? plugged in the numbers you were told for \(a=8,b=4,d=22\)

Answer 41

yes

Answer 42

final job is to solve this for \(e\)
do you know how to do that ? (no is a fine answer, i am just asking)

Answer 43

well, since b is similar to e, wouldn't e= 4 also ?

Answer 44

no

Answer 45

if they were "congruent' it would be 4

Answer 46

oh

Answer 47

you gotta solve this \[\large \frac{4}{8}=\frac{e}{22}\] for \(e\)

Answer 48

if the sides of both triangles were the same, you would have nothing to do
in these problems you have to solve the ratios
if you do not know how i will tell you

Answer 49

how would i solve the ratio to find e ?

Answer 50

is it clear that 4 is half of 8?

Answer 51

yes

Answer 52

that means \(e\) must be half of 22

Answer 53

so e= 11 ?

Answer 54

right since \[\frac{4}{8}=\frac{11}{22}=\frac{1}{2}\]

Answer 55

wanna do another?

Answer 56

yes, can we do: Find f, if c=2 1/2, d=24, a=10

Answer 57

ok we need a ratio involving \(f, c, d, a\)

Answer 58

okayy.. so would it be

2 1/2 f
---- ---
24 10

Answer 59

hold on let me check

Answer 60

okay

Answer 61

no i don't think so
let me write one

Answer 62

okay

Answer 63

or let me ask you this'
what is \(\frac{f}{d}\) equal to in the other triangle (just with the letters, forget the numbers)

Answer 64

c/a ?

Answer 65

yes !

Answer 66

now lets put the numbers in

Answer 67

sorry i dont know how you make into a fraction lol so i had to do that

Answer 68

i will do it, don't fret

Answer 69

\[\frac{f}{24}=\frac{2\tfrac{1}{2}}{10}\]

Answer 70

i just plugged in the numbers, hope i did it correctly it is hard to keep track

Answer 71

ohhh okay i see what i did wrong the first time

Answer 72

now we have to solve this for \(f\) right?

Answer 73

yes

Answer 74

i.e. we have to get rid of the \(24\) in the denominator by multiplying both sides by \(24\)

Answer 75

\[\frac{f}{24}=\frac{2\tfrac{1}{2}}{10}\\
f=24\times \frac{2\tfrac{1}{2}}{10}\]

Answer 76

mixed numbers suck to work with
unless you can do \(24\times 2\tfrac{1}{2}\) in your head

Answer 77

I cant lol

Answer 78

actually you can
two times twenty four is forty eight, half of twenty four is twelve and forty eight plus twelve is sixty
but lets do it the math teacher way

Answer 79

haha okay

Answer 80

lol

Answer 81

turn \(2\tfrac{1}{2}\) in to an improper fraction \[2\tfrac{1}{2}=\frac{5}{2}\] then \[24\times \frac{5}{2}=12\times 5=60\] as promised