Rectangle abcd is dilated to create rectangle a'b'c'd' . the width of rectangle abcd is 12 feet. the width of rectangle a'b'c'd' is 8 feet. the area of rectangle abcd is 72 square feet. what is the area of rectangle a'b'c'd' ? square feet

The area of rectangle A'B'C'D' is 32 square feet

Step-by-step explanation:

step 1

Find out the scale factor

we know that

If two figures are similar, the the ratio of its corresponding sides is proportional and this ratio is called the scale factor

Let

z ----> the scale factor

x -----> width of rectangle A'B'C'D'

y -----> width of rectangle ABCD

we have

substitute the values

Simplify

step 2

Find out the area of rectangle A'B'C'D'

we know that

If two figures are similar, the the ratio of its areas is equal to the scale factor squared

Let

z ----> the scale factor

x -----> area of rectangle A'B'C'D'

y -----> area of rectangle ABCD

we have

substitute the values

therefore

The area of rectangle A'B'C'D' is 32 square feet

32 Square Feet

Step-by-step explanation:

See picture

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