Question

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Calculate the length of LM in the isosceles right triangle ∆ KLM

Answer 1

You can use the pythagorean theorem since it has a right angle. Are you familiar with it?

Answer 2

no im kinda confused

Answer 3

do you know what a hypotenuse is?

Answer 4

yes

Answer 5

so the pythagorean theorem is:

\[ a^2 + b^2 = c^2 \]

where c is the hypotenuse. since this is an isosceles triangle, a = b, don't you think?

Answer 6

yes

Answer 7

so can you take it form here?
since a = b, \( a^2 + a^2 = c^2 \)

Answer 8

what is a and what is like what do you plug in

Answer 9

well let me ask, what is a hypotenuse?

Answer 10

the longset side of a right triangle

Answer 11

very good! which is the side *directly* across from the right angle.

so the other two sides would be 'a' and 'b', but this triangle is isosceles so a = b. therefore a is an unknown that we want to solve for and 'c' is the length of the hypotenuse

Answer 12

so if we have \(a^2 + a^2 = c^2\) where \( c = 36 \)

we only have 1 unknown so we should be able to solve this like a regular algebra problem.

Answer 13

ok

Answer 14

are you still confused? all that's left is to simplify this equation and solve.

Answer 15

okay i got 36?

Answer 16

show me your steps. i don't that's right.

Answer 17

think*

Answer 18

what is \( a^2 + a^2 \) ?

Answer 19

(@victor, please consider that the best way for a person to learn something is to have the person discover it on their own rather than just giving that person an answer.)

Answer 20

yes i need the steps!

Answer 21

there's no reason you can't do it yourself, though. you have an equation. where are you getting stuck? show me your work and i can help you.

Answer 22

can we start from the beginning im soo sorry!

Answer 23

the pythagorean theorem states that (for a right triangle):
\[ a^2 + b^2 = c^2\]where c is the hypotenuse.

we have the hypotenuse in this case, as you pointed out, and it equals 36, agree?

Answer 24

It's an isosceles triangle so it has two equal sides and therefor two equal angles. If you add the inner angles of any triangle the result will be 180º. You already know 1 angle = 90º. 180-90=90 And since the two other angles are equal you have 90/2=45. Now that you have all the angles you can use trigonometry and achieve the value of the sides. I recommend you use "sin" or "tan" (as expressed on a calculator).

Answer 25

yes

Answer 26

but this is an isosceles triangle, so the two remaining sides are equal in length, would you agree?

Answer 27

yes

Answer 28

Of course, you only need the value of one side.

Answer 29

so since the two remaining sides are \(a\) and \(b\), we know that \(a =b \)

therefore we can simplify the equation to this: \( a^2 + a^2 = c^2 \)

Answer 30

okay and c2 is 36 right so a2+a2= 36^2

Answer 31

exactly! so what does \( a^2 + a^2\) equal? we can reduce this to one term.

Answer 32

a^3

Answer 33

not quite. how about this, what does \( x + x \) equal?

Answer 34

what if i wrote it this way: \( 1x+ 1x \)

Answer 35

2x^2?

Answer 36

that wouldn't work. think about if x = 2,

1x + 1x = 1(2) + 1(2) = 4, but
2x^2 = 2(2)^2 = 8
so those two expressions are not equal.

when you add terms of the same variable, you just add their "coefficients," the number in front of the variable.

Answer 37

o okay

Answer 38

so what is x + x?

Answer 39

4

Answer 40

no x is a variable, not a number. x can be *any* number

Answer 41

okay x^2

Answer 42

no just add the numbers *in front* of the variable.

x = 1x

Answer 43

2x

Answer 44

right! so now let's look at the original equation, what is \( a^2 + a^2 \)

Answer 45

keep in mind that \(a^2 \) is the same thing as \(1a^2\)

Answer 46

2x^4

Answer 47

there are no x's in this equation. that was just as an aside example. the question here is to simplify \(a^2 + a^2\)

you know that \( x + x = 2x\), so use that same *idea* and apply it to the other equation.

Answer 48

2a^4

Answer 49

you don't add the exponents, just the coefficients.

\( x = 1x = x^1 = 1x^1 \) are all the same same

Answer 50

2a^2

Answer 51

isnt it a2=B2

Answer 52

very good! so let's look at our original equation:
\(a^2 + a^2 = 36^2 \) =
\(2a^2 = 36^2\)

Answer 53

yes it is, that's how we eliminated the b^2 and replaced it with another a^2

Answer 54

ok

Answer 55

so now our equation is \(2a^2 = 36^2\)
do you know how to solve algebra problems? that's all this is.

Answer 56

so i multiply 36 times 36 and divide it by 2

Answer 57

absolutely!

Answer 58

that would be represented like so:
\(a^2 = \frac{36^2}{2} \)
then you just take the square root of both sides to get 'a' = something

Answer 59

a^2 = 36^2 / 2

Answer 60

36 right

Answer 61

not quite, remember, it's: 36 * 36 / 2

Answer 62

ok

Answer 63

first do 36 * 36, then divide that answer by 2

Answer 64

648

Answer 65

very good!
so we're left with:
\( a^2 = 648\)

just take the square root of both sides and you have your answer!

Answer 66

i got 26

Answer 67

but thats not one of the anwsers

Answer 68

what are the answers?

Answer 69

a) 18
b) 18√2
c) 36
d) 36√2

Answer 70

well one of those answers roughly equals the number you got.

Answer 71

b

Answer 72

that's right! congrats :)

Answer 73

thanks soo much!

Answer 74

no problem :) i'm glad you wanted to learn rather than just want the answer. it'll always work out better that way. trust me ;)

Answer 75

haha thanks! :)