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Rectangle A has length 12 and width 8. Rectangle B has length 15 and width 10. Rectangle C has length 30 and width 15. Is Rectangle A a scaled copy of Rectangle B? If so, what is the scale factor? Is Rectangle B a scaled copy of Rectangle A? If so, what is the scale factor? Explain how you know that Rectangle C is not a scaled copy of Rectangle B. Is Rectangle A a scaled copy of Rectangle C? If so, what is the scale fact

Respuesta :

Rectangles are similar figures, thus if scaled copies of each other then the ratios of corresponding sides must be equal

compare ratios of lengths and widths

rectangles A and B

k = [tex]\frac{12}{15}[/tex] = [tex]\frac{4}{5}[/tex] ← ratio of lengths

k = [tex]\frac{8}{10}[/tex] = [tex]\frac{4}{5}[/tex] ← ratio of widths

scale factors are equivalent, hence rectangle A is a scaled copy of B

rectangles C and B

k = [tex]\frac{15}{30}[/tex] = [tex]\frac{1}{2}[/tex] ← ratio of lengths

k = [tex]\frac{10}{15}[/tex] = [tex]\frac{2}{3}[/tex] ← ratio of width

scale factors (k ) are not equal, hence C is not a scaled copy of B

rectangles A and C

k = [tex]\frac{30}{12}[/tex] = [tex]\frac{5}{2}[/tex] ← ratio of lengths

k = [tex]\frac{15}{8}[/tex] ← ratio of widths

the scale factors are not equal hence A is not a scaled copy of C


facundo3141592

For two rectangles, one of length L and width W, and other of length L' and width W', the second is a rescale of the first one only if exists a real number k such that:

L' = k*L

W' = k*W

Here we know:

  • Rectangle A: length = 12, width = 8
  • Rectangle B: length = 15, width = 10
  • Rectangle C: length = 30, width = 15

Let's see if rectangle A is a scaled copy of rectangle B.

To see this, we just must see if the quotients between the lengths and between the widths are equal:

15/12 = 1.25

10/8 =  1.25

Then yes, rectangle A is a rescaled copy of rectangle B, and the scale factor is k = 1.25

Is rectangle B a rescaled copy of rectangle A?

Obviously yes. The scale factor will be the inverse of the previous one, we will get:

k = 1/1.25 = 0.8

How we do know that rectangle C is not a scaled copy of rectangle B?

Because the length of C is twice the length of B, but the width of C is not twice the width of B.

Is rectangle A a scaled copy of rectangle C?

No, as we already see that rectangle C is not a rescaled copy of rectangle B, and we know that rectangle A is a rescaled copy of rectangle B.

If you want to learn more you can read:

https://brainly.com/question/20449840

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