## Gabylovesyou one year ago FInd the perimeter of the image

1. Gabylovesyou

37 units 38 units 39 units 40 units

2. Gabylovesyou

@ash2326 @phi

3. ganeshie8

to find the perimeter of given shape, you need to find out sides first

4. ganeshie8

perimeter = sum of all sides

5. ganeshie8

know how to find the length of sides on coordinate plane ?

6. Gabylovesyou

distance formula ?

7. ganeshie8

yes, but for that u need to figure out coordinates of points and plug them in the formula... which is a pain... and u need to do it for 5 times... since u have 5 sides

8. ganeshie8

there is a simpler way to do this, which uses the distance formula in disguise...

9. Gabylovesyou

ok..

10. Gabylovesyou

whats the simpler way ?

11. ganeshie8

12. ganeshie8

use pythagorean theorem : that red side = $$\sqrt{2^2+6^2} = \sqrt{40}$$

13. ganeshie8

this is exact same as distance formula, but this is felt simple because, you're not plugging in the coordinates... instead you're just counting the number of grids...

14. ganeshie8

use whichever u feel is easy...

15. Gabylovesyou

how did u solve that ^ ... like how did u get 40 ?

16. ganeshie8

the goal is to find the length of all sides and add up

17. Gabylovesyou

ok..

18. ganeshie8

did u get how I got : red side = $$\sqrt{2^2+6^2}$$

19. ganeshie8

?

20. Gabylovesyou

i know how u got the 2 and the 6... just not the 40 ...

21. ganeshie8

oh cool :) ive just skipped a step : red side = $$\sqrt{2^2+6^2} = \sqrt{4+36} = ?$$

22. Gabylovesyou

ohhh ok

23. ganeshie8

find the lengths of remaining sides in any way u wish, and add them all up

24. Gabylovesyou

for pt it would be 4^2 + 10^2

25. Gabylovesyou

which is 116

26. ganeshie8

Yes ! dont forget the sqrt

27. Gabylovesyou

ok...

28. ganeshie8

$$PT^2 = 4^2 + 10^2$$ $$PT = \sqrt{4^2 + 10^2} = \sqrt{116}$$

29. Gabylovesyou

TS is 7

30. Gabylovesyou

how do i do SR O.o

31. ganeshie8

32. Gabylovesyou

50 ok..

33. ganeshie8

*sqrt...

34. Gabylovesyou

right... lol and then the last side is sqrt 61 ?

35. Gabylovesyou

do i add them all ?

36. ganeshie8

yup ! perimeter = length around a shape = sum of all sides

37. Gabylovesyou

sqrt 274

38. Gabylovesyou

?

39. ganeshie8

lol no

40. ganeshie8

41. ganeshie8

$$\large \sqrt{a} + \sqrt{b} + \sqrt{c} ~ \ne ~ \sqrt{a + b+ c}$$

42. ganeshie8
43. Gabylovesyou

hm i got 60 ;/

44. ganeshie8

You got : $$QP = \sqrt{40}$$ $$PT = \sqrt{116}$$ $$TS = 7$$ $$SR = \sqrt{50}$$ $$RQ = \sqrt{61}$$

45. ganeshie8

right ?

46. Gabylovesyou

yes

47. ganeshie8

plug each sqrt in ur calcualtor and add them all

48. ganeshie8

$$QP = \sqrt{40} = \color{red}{6.32}$$ $$PT = \sqrt{116} = \color{red}{10.77}$$ $$TS = 7 = \color{red}{7}$$ $$SR = \sqrt{50} = \color{red}{7.07}$$ $$RQ = \sqrt{61} = \color{red}{7.81}$$ --------------------------------------- perimeter = $$\color{Red}{?}$$

49. Gabylovesyou

38. 97

50. ganeshie8
51. Gabylovesyou

so should i put 39 ?

52. Gabylovesyou

or try it the long way to double check

53. ganeshie8

rounding it becomes : $$38.97 \approx 39$$

54. ganeshie8

Nope, both are one and same... you may try for practice if u want maybe :)

55. Gabylovesyou

okay :) thank you!

56. ganeshie8

np :)