Part A :

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'

Ierofanga [76]

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

Step-by-step explanation:

A dilation is a transformation that produces an image that is the

same shape as the original, but is a different size

A dilation stretches or shrinks the original figure

The figure and its image after dilation are similar

If two rectangles are similar, then

$\frac{w_{1}}{w_{2}}=\frac{l_{1}}{l_{2}}$ = constant ratio
$\frac{P_{1}}{P_{2}}=\frac{w_{1}}{w_{2}}$
$\frac{A_{1}}{A_{2}}=(\frac{w_{1}}{w_{2}})^{2}$

∵ Rectangle ABCD is dilated to create rectangle A'B'C'D'

∴ Rectangle ABCD is similar to rectangle A'B'C'D'

∵ The width of rectangle ABCD is 12 feet

∵ The width of rectangle A'B'C'D' is 8 feet

∴ $\frac{w_{1}}{w_{2}}=\frac{12}{8}$

- Simplify the ratio to its lowest term by divide up and down by 4

∴ $\frac{w_{1}}{w_{2}}=\frac{3}{2}$

∴ The scale factor of dilation is $\frac{3}{2}$

Let us use the rule of the similar rectangles above

∵ The area of rectangle ABCD is 72 square feet

∵ $\frac{A_{1}}{A_{2}}=(\frac{w_{1}}{w_{2}})^{2}$

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

∴ $\frac{72}{A_{2}}=\frac{9}{4}$

- By using cross multiplication

∴ $A_{2}$ × 9 = 72 × 4

∴ 9 $A_{2}$ = 288

- Divide both sides by 9

∴ $A_{2}$ = 32 feet²

∴ The area of rectangle A'B'C'D' = 32 feet²

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

Learn more:

You can learn more about area of shapes in brainly.com/question/6530759

#LearnwithBrainly

3 0

3 years ago

Read 2 more answers

Hello! Please help I will rate five stars and say thank you

Morgarella [4.7K]

Answer: (C) 7x + 11x =90

Step-by-step explanation: The angle is a right angle which means that it equals 90 degrees so both angles in the right angle will add up to 90 degrees.

4 0

3 years ago

Read 2 more answers

What is the domain and range?

MrRissso [65]

Hello from MrBillDoesMath!

Answer:

Domain = { 5. 10. 15. 20}

Range = -3,-1,1,3} .

Discussion:

The domain is the set of all "x" values, that is { 5. 10. 15. 20} and the range is (-3,-1,1,3} . The arrows in the diagram show the mapping between the domain and the range. For examples, 5 -> 1 ( "x value 5 is mapped to y value 1"), 10 ->3, 15 ->-3, and 20 -> -2

Thank you,

MrB

7 0

3 years ago

Pencils come in packages of 10.Erasers come in packages of 12. Phillips wants to purpose the smallest number of pencils and eras

balandron [24]

Answer:

The answer to your question is:

Packages of pencils = 6

Packages of erasers = 5

Step-by-step explanation:

Data

Pencils = 10/package

Erasers = 12 / package

Process

Find the least common factor of 10 and 12

10 12 2

5 6 2

5 3 3

5 1 5

1

LCF = 2 x 2 x 3 x 5 = 60

Finally divide 60 by the number of pencils or erasers in each package

Packages of pencils = 60/10 = 6

Packages of erasers = 60/12 = 5

5 0

3 years ago

Brian’s kite is flying above a field at the end of 65m of string. If the angle of elevation to the kite measures 70; how high is

REY [17]

If the height is h, then h/65=sin70, so h=65sin70=61.08m approx.

7 0

3 years ago