Joshuam1
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
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Joshuam1
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the triangle
srossd
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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.
Joshuam1
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wow that was simple O_O
Joshuam1
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I have some similar questions. Think you can have a look?
srossd
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Absolutely
Joshuam1
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Quadrilateral HIJK is the pre-image of quadrilateral LMNO. Find the scale factor, t.
Joshuam1
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Joshuam1
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the options are 9/4 , 5/3, 9/25, 3/2
srossd
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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.
Joshuam1
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okay i have another I'm just working out what you said so i can have it for myself
srossd
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Okay, let me know if you have any questions.
Joshuam1
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Find WZ if the area of trapezoid ABCD is 225 cm2, the area of trapezoid WXYZ is 81 cm2, and AD is 35 cm.
Joshuam1
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21 cm
12.6 cm
58.3 cm
97.2 cm
srossd
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So, find the scale factor first, like I did in the last question.
Joshuam1
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okay :D
Joshuam1
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2.77
srossd
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Not quite, you forgot to take the square root.
Joshuam1
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find the sqrt of 2.77?
srossd
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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.
Joshuam1
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the sqrt is 1.66
srossd
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Right, so now use that to find WZ.
Joshuam1
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how?
srossd
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AB/WZ = 1.66
Joshuam1
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35/21 =1.66
srossd
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Right, so WZ = 21. Good job!
Joshuam1
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:D sweet 2 more questions
Joshuam1
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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
Joshuam1
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216 cm^2
108 cm^2
54 cm^2
24 cm^2
srossd
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Well, with those choices, it's pretty obvious. It has to be less than 54. But still, try and work it out.
Joshuam1
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okay :D what is the first step?
srossd
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Square the scale factor,s ince you're working with area.
Joshuam1
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2.25
srossd
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Right. Now, you're going from post image to pre-image, so you have to divide by that.
Joshuam1
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oh okay
Joshuam1
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so square 54?
Joshuam1
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2916
Joshuam1
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wait oops my mistake
srossd
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Are you doing 54/2.25?
Joshuam1
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sorry no i divded 54 and 3/2
srossd
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You need to divide by the squared ratio, since you're dealing with area.
Joshuam1
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alright i got 24
srossd
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Yup, nice job
Joshuam1
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ty for all your help I am done :D
srossd
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Great, no problem