safia21
  • safia21
− Calculate the length of LM in the isosceles right triangle ∆ KLM
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
safia21
  • safia21
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heisenberg
  • heisenberg
You can use the pythagorean theorem since it has a right angle. Are you familiar with it?
safia21
  • safia21
no im kinda confused

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heisenberg
  • heisenberg
do you know what a hypotenuse is?
safia21
  • safia21
yes
heisenberg
  • heisenberg
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?
safia21
  • safia21
yes
heisenberg
  • heisenberg
so can you take it form here? since a = b, \( a^2 + a^2 = c^2 \)
safia21
  • safia21
what is a and what is like what do you plug in
heisenberg
  • heisenberg
well let me ask, what is a hypotenuse?
safia21
  • safia21
the longset side of a right triangle
heisenberg
  • heisenberg
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
heisenberg
  • heisenberg
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.
safia21
  • safia21
ok
heisenberg
  • heisenberg
are you still confused? all that's left is to simplify this equation and solve.
safia21
  • safia21
okay i got 36?
heisenberg
  • heisenberg
show me your steps. i don't that's right.
heisenberg
  • heisenberg
think*
heisenberg
  • heisenberg
what is \( a^2 + a^2 \) ?
heisenberg
  • heisenberg
(@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.)
safia21
  • safia21
yes i need the steps!
heisenberg
  • heisenberg
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.
safia21
  • safia21
can we start from the beginning im soo sorry!
heisenberg
  • heisenberg
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?
anonymous
  • anonymous
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).
safia21
  • safia21
yes
heisenberg
  • heisenberg
but this is an isosceles triangle, so the two remaining sides are equal in length, would you agree?
safia21
  • safia21
yes
anonymous
  • anonymous
Of course, you only need the value of one side.
heisenberg
  • heisenberg
so since the two remaining sides are \(a\) and \(b\), we know that \(a =b \) therefore we can simplify the equation to this: \( a^2 + a^2 = c^2 \)
safia21
  • safia21
okay and c2 is 36 right so a2+a2= 36^2
heisenberg
  • heisenberg
exactly! so what does \( a^2 + a^2\) equal? we can reduce this to one term.
safia21
  • safia21
a^3
heisenberg
  • heisenberg
not quite. how about this, what does \( x + x \) equal?
heisenberg
  • heisenberg
what if i wrote it this way: \( 1x+ 1x \)
safia21
  • safia21
2x^2?
heisenberg
  • heisenberg
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.
safia21
  • safia21
o okay
heisenberg
  • heisenberg
so what is x + x?
safia21
  • safia21
4
heisenberg
  • heisenberg
no x is a variable, not a number. x can be *any* number
safia21
  • safia21
okay x^2
heisenberg
  • heisenberg
no just add the numbers *in front* of the variable. x = 1x
safia21
  • safia21
2x
heisenberg
  • heisenberg
right! so now let's look at the original equation, what is \( a^2 + a^2 \)
heisenberg
  • heisenberg
keep in mind that \(a^2 \) is the same thing as \(1a^2\)
safia21
  • safia21
2x^4
heisenberg
  • heisenberg
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.
safia21
  • safia21
2a^4
heisenberg
  • heisenberg
you don't add the exponents, just the coefficients. \( x = 1x = x^1 = 1x^1 \) are all the same same
safia21
  • safia21
2a^2
safia21
  • safia21
isnt it a2=B2
heisenberg
  • heisenberg
very good! so let's look at our original equation: \(a^2 + a^2 = 36^2 \) = \(2a^2 = 36^2\)
heisenberg
  • heisenberg
yes it is, that's how we eliminated the b^2 and replaced it with another a^2
safia21
  • safia21
ok
heisenberg
  • heisenberg
so now our equation is \(2a^2 = 36^2\) do you know how to solve algebra problems? that's all this is.
safia21
  • safia21
so i multiply 36 times 36 and divide it by 2
heisenberg
  • heisenberg
absolutely!
heisenberg
  • heisenberg
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
heisenberg
  • heisenberg
a^2 = 36^2 / 2
safia21
  • safia21
36 right
heisenberg
  • heisenberg
not quite, remember, it's: 36 * 36 / 2
safia21
  • safia21
ok
heisenberg
  • heisenberg
first do 36 * 36, then divide that answer by 2
safia21
  • safia21
648
heisenberg
  • heisenberg
very good! so we're left with: \( a^2 = 648\) just take the square root of both sides and you have your answer!
safia21
  • safia21
i got 26
safia21
  • safia21
but thats not one of the anwsers
heisenberg
  • heisenberg
what are the answers?
safia21
  • safia21
a) 18 b) 18√2 c) 36 d) 36√2
heisenberg
  • heisenberg
well one of those answers roughly equals the number you got.
safia21
  • safia21
b
heisenberg
  • heisenberg
that's right! congrats :)
safia21
  • safia21
thanks soo much!
heisenberg
  • heisenberg
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 ;)
safia21
  • safia21
haha thanks! :)

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