SOLUTION: Tristan is working on dilating rectangles. Rectangle ABCD is dilated by a factor of 3. The resulting rectangle WXYZ has an area of 72 cm2. Tristan found that the area of rectangl

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Question 1152338: Tristan is working on dilating rectangles. Rectangle ABCD is dilated by a
factor of 3. The resulting rectangle WXYZ has an area of 72 cm2. Tristan
found that the area of rectangle ABCD must be 8 cm2. Is he correct?
A. No, because he needs to divide the area of rectangle WXYZ by 3.
B. No, because he needs to multiply the area of rectangle WXYZ by 3.
C. Yes, because he needs to find the possible dimensions for rectangle
WXYZ and then divide each dimension by 3.
D. Yes, because he needs to find the possible dimensions for rectangle
WXYZ and then multiply each dimension by 3.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

If the area of the resulting rectangle is 72 cm^2, then the area of the original rectangle is  1%2F9  of that,

i.e. 72%2F9 = 8 cm^2.

Solved and answered.

All these arguments under each option are non-sensical, and reading them may harm mental health of a reader.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


When a figure (any shape!) is dilated by a factor of 3, the scale factor (ratio of linear measurements) between the original figure and the dilated figure is 3:1.

If the scale factor between two similar figures is 3:1, then the ratio of the areas is the square of that, which is 9:1. If the figure were 3-dimensional, then the ratio of volumes would be the cube of the scale factor, which would be 27:1.

Tristan's answer is right, because 72/9 = 8.

None of the answer choices is correct.

Answer choices A and B are both wrong, because they say Tristan's answer is wrong.

Answer choice D is wrong, because it says the dimensions of the original rectangle have to be multiplied by 3.

And answer choice C, while closest to being correct, is still not right, because THERE IS NO NEED TO FIND/GUESS THE DIMENSIONS OF THE ORIGINAL TRIANGLE, DIVIDE THEM BOTH BY 3, AND THEN MULTIPLY THE NEW DIMENSIONS TO FIND THE NEW AREA.

The only thing he needs to do is divide the area of the original rectangle by 3^2=9.

So Tristan's answer is right; and none of the given answer choices is correct.