Question

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Answer 1

ABC is an isoceles triangle
angle ABC=angle ACB=47 degree

Answer 2

AD is perependicular? @https.wild_

Answer 3

AD is perpendicular to ABC and ACB yes.

Answer 4

Or, wait would they be because AD is the same as AB and AC..so i would say no that AD is not perpendicular to ABC and ACB..right?

Answer 5

why is AD same as AB?

Answer 6

Because they are both parallel they are both going down..

Answer 7

they are not parallel

Answer 8

Why not? Is it because AD is the middle and AB is more on the outside?

Answer 9

parallel means the angle between them is 180 degrees

Answer 10

OHH, and AB and AC is 47 degrees correct?

Answer 11

angle ABC=angle ACB=47 degrees

Answer 12

now lets consider triangle ABC
angle A=y+y=2y
and the sum of the three angles of a triangle is 180 degrees so
2y+47+47=180
or 2y=180-47-47=86 implies y=43

Answer 13

you did 86/2y and got 43 right?

Answer 14

yeah

Answer 15

now in triangle ABD,
y+x+47=180 implies x=180-y-47=180-43-47=90

Answer 16

so x=90 and y=43

Answer 17

oh so i just needed to subtract -43 and -47 of 180 to get 90 which is x correct?

Answer 18

correct

Answer 19

Thank you that sort of makes sense.

Answer 20

Yeah thank you! Arigato ( means thank you in Japanese ) c: Could you perhaps help me with another one? It's just this one doesn't have a triangle..its just letters. which is confusing to me.

Answer 21

ok give me the question

Answer 22

see for isoscele any two sides must be equal

Answer 23

first let 3x=5x-12

Answer 24

then 2x=12 implies x=6
then the sides will be 3.6,5.6-12,6+20 i.e. 18,18, 26

Answer 25

wait wait

Answer 26

for a triangle, the length of any two sides must be greater than the third side. see 18+18>26, 18+26>18 and 26+18>18
so x=6 is a possibility

Answer 27

You subtracted 3x of 5x correct? Which equals 2x and then why is 6 a possibility? is it because it can multiple 18?

Answer 28

i meant 5x-3x

Answer 29

yeah

Answer 30

Okay, out of this information what do we do next?

Answer 31

we got x.

Answer 32

x=6

Answer 33

now lets see if the other possibilites are true or not

Answer 34

Okay..i am confused to what you are trying to tell me here..

Answer 35

@https.wild_

Answer 36

You just confused me..x.x

Answer 37

ok for isosceles triangle, any two sides will be equal right?

Answer 38

@https.wild_

Answer 39

Right!

Answer 40

what are the given sides here???

Answer 41

The given sides are 3x, 5x-12 and x+20

Answer 42

or wait..those are the lengths of the sides..

Answer 43

so the length of any two of them must be equal for the triangle to be isosceles???

Answer 44

okay, so does that mean we need to find one more length? since we are found that 3x=5x-12 which equals 6x

Answer 45

no.. any two of them will be equal. but we dont know which of the two are equal.
so we will consider 3 cases

Answer 46

case 1) the first two lengths are equal
then 3x=5x-12 implies 5x-3x=12 implies 2x=12 implies x=6

Answer 47

case 2) the second and third lengths are equal
then 5x-12=x+20
implies 5x-x=20+12
implies 4x=32 implies x=32/4=8

Answer 48

case 3) the third and first length are equal then x+20=3x
implies 3x-x=20implies 2x=20 implies x=20/2=10

Answer 49

@https.wild_

Answer 50

They all equal different numbers, so none of them are equal and we need two equal sides

Answer 51

yah

Answer 52

x is not the length of side

Answer 53

now we have to determine which value of x we can take

Answer 54

i.e. x=6, or 8 or 10

Answer 55

Do we just pick any number?..

Answer 56

no

Answer 57

like we can pick any of those three?

Answer 58

we have to do a test

Answer 59

For a triangle, the length of any two sides must be greater than the third side

Answer 60

now in Case 1) we calculate the length of the sides
here we got x=6
the lengths are 3x,5x-12 and x+20
i.e. 3.6,5.6-12,6+20
i.e. 18,18,26
check here that the length of any two sides is greater than the third side. so x=6 makes the triangle isosceles

Answer 61

HOW DO YOU KNOW THAT? o-o How do you know it makes the triangle isosceles, you said" for isosceles triangle, any two sides will be equal " what makes x=6 equal?

Answer 62

put x=6 in the given lengths

Answer 63

what do you get the lengths then?

Answer 64

3x and 5x-12 both equal 18 but x+20 equals 26 so 3x and 5x-12 is what makes the triangle an isosceles right?

Answer 65

yeah

Answer 66

similarly check for case 2 when x=8 what are the lengths?

Answer 67

3(8)=24
5(8)-12=28
(8)+20=28

Answer 68

so x=8 also gives isosceles triangle
finally check for x=10