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

Mathematics
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You can use the pythagorean theorem since it has a right angle. Are you familiar with it?
no im kinda confused

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Other answers:

do you know what a hypotenuse is?
yes
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?
yes
so can you take it form here? since a = b, \( a^2 + a^2 = c^2 \)
what is a and what is like what do you plug in
well let me ask, what is a hypotenuse?
the longset side of a right triangle
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
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.
ok
are you still confused? all that's left is to simplify this equation and solve.
okay i got 36?
show me your steps. i don't that's right.
think*
what is \( a^2 + a^2 \) ?
(@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.)
yes i need the steps!
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.
can we start from the beginning im soo sorry!
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?
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).
yes
but this is an isosceles triangle, so the two remaining sides are equal in length, would you agree?
yes
Of course, you only need the value of one side.
so since the two remaining sides are \(a\) and \(b\), we know that \(a =b \) therefore we can simplify the equation to this: \( a^2 + a^2 = c^2 \)
okay and c2 is 36 right so a2+a2= 36^2
exactly! so what does \( a^2 + a^2\) equal? we can reduce this to one term.
a^3
not quite. how about this, what does \( x + x \) equal?
what if i wrote it this way: \( 1x+ 1x \)
2x^2?
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.
o okay
so what is x + x?
4
no x is a variable, not a number. x can be *any* number
okay x^2
no just add the numbers *in front* of the variable. x = 1x
2x
right! so now let's look at the original equation, what is \( a^2 + a^2 \)
keep in mind that \(a^2 \) is the same thing as \(1a^2\)
2x^4
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.
2a^4
you don't add the exponents, just the coefficients. \( x = 1x = x^1 = 1x^1 \) are all the same same
2a^2
isnt it a2=B2
very good! so let's look at our original equation: \(a^2 + a^2 = 36^2 \) = \(2a^2 = 36^2\)
yes it is, that's how we eliminated the b^2 and replaced it with another a^2
ok
so now our equation is \(2a^2 = 36^2\) do you know how to solve algebra problems? that's all this is.
so i multiply 36 times 36 and divide it by 2
absolutely!
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
a^2 = 36^2 / 2
36 right
not quite, remember, it's: 36 * 36 / 2
ok
first do 36 * 36, then divide that answer by 2
648
very good! so we're left with: \( a^2 = 648\) just take the square root of both sides and you have your answer!
i got 26
but thats not one of the anwsers
what are the answers?
a) 18 b) 18√2 c) 36 d) 36√2
well one of those answers roughly equals the number you got.
b
that's right! congrats :)
thanks soo much!
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 ;)
haha thanks! :)

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