1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Soloha48 [4]
3 years ago
7

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' ?

Mathematics
2 answers:
frosja888 [35]3 years ago
6 0

32 square feet

<h3>Further explanation</h3>

<u>Given:</u>

  • 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.

<u>Question:</u>

What is the area of rectangle A'B'C'D' ?

<u>The Process:</u>

The Similarity Ratio

We calculate the similarity ratio of the two widths given.

Let the width of the rectangle ABCD  as AD and the width of the rectangle A'B'C'D 'as A'D'.

\boxed{ \ The \ Similarity \ Ratio = k = \frac{A'D'}{AD} \ }

\boxed{ \ k = \frac{8}{12} \ } \rightarrow \boxed{ \ k = \frac{2}{3} \ }

Next to calculate the area of the rectangle A'B'C'D', let us do it in two ways. You can choose one of them.

<u>First Way:</u>

The relationship between the area of ABCD and the area of A'B'C'D' is as follows:

\boxed{ \ The \ area \ of \ A'B'C'D' = k^2 \times the \ area \ of \ ABCD \ }

\boxed{ \ The \ area \ of \ A'B'C'D' = \big( \frac{2}{3} \big)^2 \times 72 \ square \ feet \ }

\boxed{ \ The \ area \ of \ A'B'C'D' = \frac{4}{9} \times 72 \ square \ feet \ }

Thus, the area of rectangle A'B'C'D' is 32 square feet.

<u>Second Way:</u>

Let us find out the length of ABCD, we just call it AB.

\boxed{ \ Length \times width = the \ area \ of \ rectangle \ ABCD \ }

\boxed{ \ Length \times 12 \ feet = 72 \ square \ feet \ }

\boxed{ \ Length = (72 \div 12) \ feet \ }

\boxed{ \ Length \ of \ AB = 6 \ feet \ }

Next, we find out the length of A'B'C'D', we just call it A'B'. Use the similarity ratio.

\boxed{ \ The \ Similarity \ Ratio = k = \frac{A'B'}{AB} \ }

\boxed{ \ \frac{A'B'}{6} = \frac{2}{3} \ }

Therefore, the length of A'B' is 4 feet.

And then, we calculate the area of A'B'C'D'.

\boxed{ \ The \ area \ of \ rectangle \ A'B'C'D' = length \times width \ }

\boxed{ \ The \ area \ of \ rectangle \ A'B'C'D' = 4 \ feet \times 8 \ feet \ }

Thus, the area of rectangle A'B'C'D' is 32 square feet.

<h3>Learn more</h3>
  1. About shifting and stretching brainly.com/question/11384371
  2. The similar problem of shifting brainly.com/question/2488474  
  3. Which phrase best describes the translation from the graph y = 2(x – 15)2 + 3 to the graph of y = 2(x – 11)2 + 3? brainly.com/question/1369568

Keywords: rectangle ABCD, dilated, to create, A'B'C'D', the width, 12 feet, the area, 72 square, 32, the similarity ratio, length, ways

#learnwithBrainly

Ierofanga [76]3 years ago
3 0

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

You might be interested in
2.<br> - 4x + 9y = 14<br> 12x – 10y = -8<br> ;<br> multiplication
NeTakaya

Answer:

Step-by-step explanation: (Equation 2) = 12(-12+9y/4) - 10y = -8

-144+108y/4 - 10y = -8

-144 + 108y - 40y/4 = -8

-144 + 108y - 40y = -32

108y - 40y = -32+144

68y = 112

Y= 1.64

2-4x+9y=14

12x-10y= -8

2-14+9y = 4x

-12 + 9y = 4x ( equation 3)

(Put in equation 2)

3 0
2 years ago
Read 2 more answers
X+4y=4 y in terms of x
Alinara [238K]

Answer:

x + 4y = 4

4y = 4 - x

multiply both sides by 1/4

y = 1/4( 4- x)

y = 1- 1/4x

3 0
2 years ago
Read 2 more answers
Which relation is a function?
aksik [14]

Answer:

B

Step-by-step explanation:

5 0
2 years ago
A little help over here please appreciate all
sweet [91]

Answer:

hello i dont know that answer

Step-by-step explanation:

but i hope ypu have a nice day stay nice byeeee

6 0
3 years ago
Read 2 more answers
Please help soon!!!!!
Ronch [10]
The answer is 96in because is you multiply 8x2x6= 96
4 0
2 years ago
Other questions:
  • Which number should follow in this series: 64/64 9/12 6/12​
    12·2 answers
  • Emma divided the trapezoid into two triangles to find the area​
    10·1 answer
  • I already got the answer, here's free points I guess :/
    11·2 answers
  • Which term best describes a major arc of a circle that has the same starting and ending point
    7·2 answers
  • Kevin will take 4 math tests this term. All of the tests are worth the same number of points. After taking the first 3 tests, hi
    7·2 answers
  • how much carrots can a rabbit chuck chuck if a rabbit could chuck carrots Lol this is random but ill mark Brainliest if you put
    13·1 answer
  • I need help answer 6 through 7 I can't figure them out
    11·1 answer
  • What is 52% as a decimal
    13·2 answers
  • Select all the statements about the situation that are true. Elena makes more money for making 10 calls than Diego makes for was
    8·1 answer
  • Can someone figure out how to do this I don't know how.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!