Mathematics, 05.07.2019 01:00 juter92

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

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Answer from: peno211

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 = 8Rectangle B: length = 15, width = 10Rectangle 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:

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Answer from: briannawoods13

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 = $\frac{12}{15}$ = $\frac{4}{5}$ ← ratio of lengths

k = $\frac{8}{10}$ = $\frac{4}{5}$ ← ratio of widths

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

rectangles C and B

k = $\frac{15}{30}$ = $\frac{1}{2}$ ← ratio of lengths

k = $\frac{10}{15}$ = $\frac{2}{3}$ ← ratio of width

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

rectangles A and C

k = $\frac{30}{12}$ = $\frac{5}{2}$ ← ratio of lengths

k = $\frac{15}{8}$ ← ratio of widths

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

Answer from: Quest

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Answer from: Quest

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step-by-step explanation:

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Rectangle a has length 12 and width 8. rectangle b has length 15 and width 10. rectangle c has lengt...