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
Please answer this asap
Oduvanchick [21]

Answer:

the second on

Step-by-step explanation:

7 0
2 years ago
I have 6 surfaces 2 of my surfaces are smaller then the others I can stand up tall what shape am I
Arada [10]
This shape would be a rectangular prism, with 4 rectangular sides, and 2 square or smaller rectangular sides.

An example of a rectangular prism would be a brick. It has 4 sides that are perfectly alike, then two other sides that are like each other.
5 0
3 years ago
Read 2 more answers
A flat surface of a solid figure
mylen [45]
Rectangualr prism solid figure can be made woth more than 1 shape
7 0
3 years ago
Read 2 more answers
50 apple's cost $25. How much would 75 apples cost?
8_murik_8 [283]

Answer:

$37.5

Step-by-step explanation:

(25/50) x 75 = 37.5

$25/50  .... each apple cost $0.5

0.5 x 75 = 37.5

8 0
3 years ago
Answer this please due in a hour
horrorfan [7]

Answer: 1. b=-3/2 or -1 1/2

2. B=17/3 or 5 2/3

3. K=-14

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • How much will you save if you buy an item listed at $575.50 at a 30 percent discount?
    5·2 answers
  • A cell phone company has a basic monthly plan of 40$ plus $0.45 for any minutes uses over 700. Before receiving this statement,
    12·2 answers
  • Solve for c.
    11·2 answers
  • What is p(9)?what the percentage
    12·1 answer
  • A categorical variable whose values are purely qualitative and unordered is called a _______ variable. Please type the correct a
    8·1 answer
  • Convert 5.4 ⋅ 103 to standard form. 0.0054 0.00054 5,400 54,000
    8·2 answers
  • Abigail needs at least $199 to purchase the new phone that she wants. Last week she babysat and earned $45. Write and solve an i
    13·1 answer
  • 10 p<br> Find the measure of the indicated angle. Round to the nearest degree.<br> 46<br> 12
    15·1 answer
  • Can you help me find the code<br><br><br><br> link/picture in the comments
    8·2 answers
  • Problem below<br><br> Please show full work <br><br> Thx
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!