Mathematics, 04.11.2019 20:31 kris1920

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

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Answer from: hernandezbrandon059

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

$z=\frac{x}{y}$

we have

$x=8\ ft\\y=12\ ft$

substitute the values

$z=\frac{8}{12}$

Simplify

$z=\frac{2}{3}$

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

$z^2=\frac{x}{y}$

we have

$y=72\ ft^2$

$z=\frac{2}{3}$

substitute the values

$(\frac{2}{3})^2=\frac{x}{72}$

$\frac{4}{9}=\frac{x}{72}$

$x=\frac{4}{9}(72)\\\\ x=32\ ft^2$

therefore

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

Answer from: jtmoney10

32 Square Feet

Step-by-step explanation:

See picture

Rectangle abcd is dilated to create rectangle a'b'c'd' . the width of rectangle abcd is 12 feet. the

Answer from: Quest

it is c, trust i got your back lol

step-by-step explanation:

Answer from: Quest

the most boring thing ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.

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Rectangle abcd is dilated to create rectangle a'b'c'd' . the width of rectangle abcd is 12 feet. the...

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