## Joshuam1 2 years ago Triangle UVW is the pre-image of triangle RST with a scale factor of 3. Find the area of triangle UVW if the area of triangle RST is 9 cm2. 81 cm2 27 cm2 18 cm2 9 cm2

1. Joshuam1

the triangle

2. srossd

An intuitive way to think about this is that area is the square of distance. So, when you scale the distances of the sides by 3, the area scales by 9. So, 9 cm2 becomes 81 cm2.

3. Joshuam1

wow that was simple O_O

4. Joshuam1

I have some similar questions. Think you can have a look?

5. srossd

Absolutely

6. Joshuam1

Quadrilateral HIJK is the pre-image of quadrilateral LMNO. Find the scale factor, t.

7. Joshuam1

8. Joshuam1

the options are 9/4 , 5/3, 9/25, 3/2

9. srossd

So, 375/135 = 2.77ish. You know from the last question that that's the square of the scale factor. Square root it and you get 1.66ish. So, 5/3.

10. Joshuam1

okay i have another I'm just working out what you said so i can have it for myself

11. srossd

Okay, let me know if you have any questions.

12. Joshuam1

Find WZ if the area of trapezoid ABCD is 225 cm2, the area of trapezoid WXYZ is 81 cm2, and AD is 35 cm.

13. Joshuam1

21 cm 12.6 cm 58.3 cm 97.2 cm

14. srossd

So, find the scale factor first, like I did in the last question.

15. Joshuam1

okay :D

16. Joshuam1

2.77

17. srossd

Not quite, you forgot to take the square root.

18. Joshuam1

find the sqrt of 2.77?

19. srossd

Right, 225/81=2.77, but that's the ratio of the areas. To turn that into the ratio of lengths, you need the square root.

20. Joshuam1

the sqrt is 1.66

21. srossd

Right, so now use that to find WZ.

22. Joshuam1

how?

23. srossd

AB/WZ = 1.66

24. Joshuam1

35/21 =1.66

25. srossd

Right, so WZ = 21. Good job!

26. Joshuam1

:D sweet 2 more questions

27. Joshuam1

Find the area of the pre-image rectangle QRST if the area of the image rectangle DEFG is 54 cm^2 and the scale factor is 3/2

28. Joshuam1

216 cm^2 108 cm^2 54 cm^2 24 cm^2

29. srossd

Well, with those choices, it's pretty obvious. It has to be less than 54. But still, try and work it out.

30. Joshuam1

okay :D what is the first step?

31. srossd

Square the scale factor,s ince you're working with area.

32. Joshuam1

2.25

33. srossd

Right. Now, you're going from post image to pre-image, so you have to divide by that.

34. Joshuam1

oh okay

35. Joshuam1

so square 54?

36. Joshuam1

2916

37. Joshuam1

wait oops my mistake

38. srossd

Are you doing 54/2.25?

39. Joshuam1

sorry no i divded 54 and 3/2

40. srossd

You need to divide by the squared ratio, since you're dealing with area.

41. Joshuam1

alright i got 24

42. srossd

Yup, nice job

43. Joshuam1

ty for all your help I am done :D

44. srossd

Great, no problem