Question

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

Answer 1

32 Square Feet

Explanation:

See picture

Answer 2

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

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=(x)/(y)`

we have

`x=8\ ft\\y=12\ ft`

substitute the values

`z=(8)/(12)`

Simplify

`z=(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=(x)/(y)`

we have

`y=72\ ft^2`

`z=(2)/(3)`

substitute the values

`((2)/(3))^2=(x)/(72)`

`(4)/(9)=(x)/(72)`

`x=(4)/(9)(72)\\\\ x=32\ ft^2`

therefore

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