## safia21 Group Title − Calculate the length of LM in the isosceles right triangle ∆ KLM 2 years ago 2 years ago

1. safia21 Group Title

2. heisenberg Group Title

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

3. safia21 Group Title

no im kinda confused

4. heisenberg Group Title

do you know what a hypotenuse is?

5. safia21 Group Title

yes

6. heisenberg Group Title

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?

7. safia21 Group Title

yes

8. heisenberg Group Title

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

9. safia21 Group Title

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

10. heisenberg Group Title

well let me ask, what is a hypotenuse?

11. safia21 Group Title

the longset side of a right triangle

12. heisenberg Group Title

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

13. heisenberg Group Title

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.

14. safia21 Group Title

ok

15. heisenberg Group Title

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

16. safia21 Group Title

okay i got 36?

17. heisenberg Group Title

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

18. heisenberg Group Title

think*

19. heisenberg Group Title

what is $$a^2 + a^2$$ ?

20. heisenberg Group Title

(@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.)

21. safia21 Group Title

yes i need the steps!

22. heisenberg Group Title

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.

23. safia21 Group Title

can we start from the beginning im soo sorry!

24. heisenberg Group Title

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?

25. Victor_Hugo Group Title

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).

26. safia21 Group Title

yes

27. heisenberg Group Title

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

28. safia21 Group Title

yes

29. Victor_Hugo Group Title

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

30. heisenberg Group Title

so since the two remaining sides are $$a$$ and $$b$$, we know that $$a =b$$ therefore we can simplify the equation to this: $$a^2 + a^2 = c^2$$

31. safia21 Group Title

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

32. heisenberg Group Title

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

33. safia21 Group Title

a^3

34. heisenberg Group Title

not quite. how about this, what does $$x + x$$ equal?

35. heisenberg Group Title

what if i wrote it this way: $$1x+ 1x$$

36. safia21 Group Title

2x^2?

37. heisenberg Group Title

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.

38. safia21 Group Title

o okay

39. heisenberg Group Title

so what is x + x?

40. safia21 Group Title

4

41. heisenberg Group Title

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

42. safia21 Group Title

okay x^2

43. heisenberg Group Title

no just add the numbers *in front* of the variable. x = 1x

44. safia21 Group Title

2x

45. heisenberg Group Title

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

46. heisenberg Group Title

keep in mind that $$a^2$$ is the same thing as $$1a^2$$

47. safia21 Group Title

2x^4

48. heisenberg Group Title

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.

49. safia21 Group Title

2a^4

50. heisenberg Group Title

you don't add the exponents, just the coefficients. $$x = 1x = x^1 = 1x^1$$ are all the same same

51. safia21 Group Title

2a^2

52. safia21 Group Title

isnt it a2=B2

53. heisenberg Group Title

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

54. heisenberg Group Title

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

55. safia21 Group Title

ok

56. heisenberg Group Title

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

57. safia21 Group Title

so i multiply 36 times 36 and divide it by 2

58. heisenberg Group Title

absolutely!

59. heisenberg Group Title

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

60. heisenberg Group Title

a^2 = 36^2 / 2

61. safia21 Group Title

36 right

62. heisenberg Group Title

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

63. safia21 Group Title

ok

64. heisenberg Group Title

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

65. safia21 Group Title

648

66. heisenberg Group Title

very good! so we're left with: $$a^2 = 648$$ just take the square root of both sides and you have your answer!

67. safia21 Group Title

i got 26

68. safia21 Group Title

but thats not one of the anwsers

69. heisenberg Group Title

what are the answers?

70. safia21 Group Title

a) 18 b) 18√2 c) 36 d) 36√2

71. heisenberg Group Title

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

72. safia21 Group Title

b

73. heisenberg Group Title

that's right! congrats :)

74. safia21 Group Title

thanks soo much!

75. heisenberg Group Title

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 ;)

76. safia21 Group Title

haha thanks! :)