## anonymous one year ago A right triangle has base (x - 7) units and height (2x - 10) units. Part A: What is the square of the length of the hypotenuse of the triangle? Show your work. (4 points) Part B: What is the area of the triangle? (3 points) Part C: Using the solution obtained in Part B, explain the closure property of multiplication of polynomials. (3 points)

1. anonymous

@ganeshie8 @Nnesha @hartnn

2. anonymous

3. anonymous

@mathmate @welshfella Can you guys help? I have a general idea of what I need to do for part one, but I get really lost afterwards.

4. welshfella

square of hypotenuse , by Pythagoras theorem = sum of squares on the other 2 sides = (x - 7^2 + (2x - 10)^2

5. anonymous

I got that much, but I need to simplify it I believe

6. anonymous

@welshfella

7. kobeni-chan

What do you have that you need to simplify?

8. anonymous

I need the square length of the hypotenuse. so wouldn't I need to simplify (x-7)^2 + (2x+10)= C^2?

9. anonymous

Like I know that much but I don't know what to do afterwards. do I square everything?

10. kobeni-chan

You need to square (x-7) and (2x-10) right now. If you have a scientific calculator you can do this easily, but if you have a reg. calculator then do (x-7)(x-7) and use the distributive property. Then do the same with (2x-10)(2x-10)

11. anonymous

|dw:1433177251700:dw|

12. anonymous

|dw:1433177275411:dw|

13. anonymous

|dw:1433177299845:dw|

14. anonymous

|dw:1433177325031:dw| ?

15. anonymous

Did I do that part correct?

16. kobeni-chan

h/o

17. anonymous

Oki cx

18. kobeni-chan

Yes that's right :) sorry if I'm slow to respond I'm doing my exam

19. anonymous

Okay, so now I do (2x-10)(2x-10)?

20. kobeni-chan

Yep

21. anonymous

|dw:1433177671889:dw| Sorry for the bad writing ;-;~

22. welshfella

now had these 2 expansions together x&3 - 14x + 49 + 4x^2 - 40x + 100

23. welshfella

**correction first term is x^2

24. anonymous

25. welshfella

yes

26. anonymous

|dw:1433178085721:dw|

27. welshfella

add like terms eg x^2 + 4x^2 = 5 x^2

28. welshfella

yep

29. anonymous

is that the answer? for part A I mean

30. welshfella

yes

31. welshfella

Part B the area = 1/2 * base * height = 1/2 * (x - 7) (2x - 10)

32. anonymous

how do I do that o.O

33. anonymous

@kobeni-chan ? ;-;~

34. welshfella

to make it easier 1/2 * (2x - 10) = (x - 5) now work out (x - 7)(x - 5) and you gave the required area

35. welshfella

* have

36. anonymous

|dw:1433179051398:dw|

37. anonymous

@amistre64 @Here_to_Help15

38. anonymous

@mathstudent55 @paki @Luigi0210

39. anonymous

40. kobeni-chan

I'm so sorry I got very busy and forgot about your question :( what part are you on?

41. anonymous

Part B I believe >.>

42. anonymous

@Aureyliant >.>

43. anonymous

Ok so Pt. B is asking the area.. what is your understanding of this Q?

44. anonymous

That for the area, you need to do a=1/2*b*h since we already have b and h, we just plug it in. Right?

45. anonymous

Yup!

46. anonymous

I got that much, but when it comes to trying to find said area, I get completely lost

47. anonymous

48. anonymous

I know that much, but I don't know how to apply the 1/2 to the (x-7)

49. welshfella

you've worked it out correctly alice

50. anonymous

so is that trinomial the Area?

51. anonymous

You can either take it's inverse out, but since it's an expression & not an equation, it's like dividing (x-7) by 2.

52. welshfella

apply the half to (2x -10) first makes it easier 1/2 * (2x - 10 ) = x - 5

53. anonymous

^ Agreed

54. welshfella

so it comes down to (x -5)(x - 7) which you worked out correctly in an earlier post alice

55. anonymous

I did (x-5)(x-7). Is there no other step afterwards?

56. anonymous

Nope. You can check your work by multiplying again, and you should be getting the same answer you started with.