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
Fittoniya [83]
2 years ago
5

The shapes below are similar. Find the length x. Will mark brainliest!!!!!!

Mathematics
2 answers:
KatRina [158]2 years ago
8 0

Answer:

x = 8

Step-by-step explanation:

<u>Similar shapes</u> are <u>dilations</u> of each other using a <u>scale factor</u>.

As the area of both figures has been given, the scale factor that maps the green figure to the yellow figure can be calculated:

\implies \textsf{Scale factor (area)} = \dfrac{\textsf{area of yellow figure}}{\textsf{area of green figure}} = \sf \dfrac{352}{22} = 16

Area is measured in square units. Therefore, to find the <u>scale factor for length</u>, square root the scale factor for area:

\begin{aligned}\implies \textsf{Scale factor (length)} & = \sf \sqrt{\textsf{Scale factor for area}} \\ & =\sf \sqrt{16}\\ & = \sf 4 \end{aligned}

Use the found <u>scale factor for length</u> to find the <u>perimeter</u> of the yellow figure:

\begin{aligned} \sf \implies \textsf{Perimeter (yellow fig)} & = \sf \textsf{perimeter (green fig)} \times scale\:factor \\ & = \sf 26 \times 4 \\ & = \sf 104\: mm \end{aligned}

Find the <u>missing horizontal lengths</u> of the yellow figure by using the corresponding length of the green figure:

⇒ 4 mm × 4 = 16 mm

⇒ 24 mm - 16 mm = 8 mm

Let the <u>height of the yellow figure</u> be y.

⇒ 24 + 8 + 16 + y + x + (y - x) = perimeter

⇒ 48 + 2y = 104

⇒ 2y = 56

⇒ y = 28 mm

Divide the yellow figure into two rectangles (see attachment).

  • Area of left rectangle = y × 8 = 28 × 8 = 224 mm²
  • Area of right rectangle = 16x mm²

To find x, sum the areas of the rectangles and equate to 352:

⇒ 224 + 16x = total area

⇒ 224 + 16x = 352

⇒ 16x = 128

⇒ x = 8

sergiy2304 [10]2 years ago
3 0

The value of x is 8 mm.

<h3>What are Similar Figures ?</h3>

Similar Figures are the figures in which all the sides of one figure are in same ratio with the other side.

Two figures are given which are similar to each other .

When two figures are in ratio a:b then Area will be in ratio a² : b²

Area of figure 1 = 22 sq.mm

Area of figure 2 = 352 sq.mm

A1 :A2 = 22 /352

a² : b² = 1 / 16

a:b = 1/4

Therefore the bigger figure is 4 times the small figure .

The 4mm side will be 16 mm in the larger figure

The difference will be the value of x

x = 24 -16 = 8 mm

Therefore the value of x is 8 mm.

To know more about Similar Figures

brainly.com/question/27752055

#SPJ1

You might be interested in
The sum of 4 times a number and 9 is equal to 8. Use the variable b for the unknown number.
Alexxandr [17]
Answers
4b+9=8
This is the required statement
8 0
2 years ago
Read 2 more answers
Help plz anyone who’s good with slope?
ss7ja [257]

Answer:

-3

Step-by-step explanation:

you go down from the dot left most and you count towards the line that the second dot falls on and count over too it

5 0
2 years ago
Read 2 more answers
Student A starts with $100 in the bank and makes $5 a day. Student B starts with $50 and makes $7 a day. Assuming the students s
nasty-shy [4]
Student A starts with $100 in the bank and makes $5 a day. Student B starts with $50 and makes $7 a day. Assuming the students save their money, when will they have the same amount of money ?
3 0
3 years ago
Read 2 more answers
Which notation best represents the phrase “no more than 200”?a. 200 d.≥ 200 plz hurry i need asnwer asp
ElenaW [278]

Answer:

D it is d my guy you have fun with that

4 0
3 years ago
Can someone please help me with this question about given two points?Please help ASAP!!! :(
KonstantinChe [14]

Answer:

<em>The order of subtraction is not important in any of the coordinates</em>

Step-by-step explanation:

Distance Between Two Points

Given two points (x1,y2) (x2,y2), the distance between them is given by the formula

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

The difference between both coordinates is squared, then added, and finally extracted the square root.

Based on the principle that

a*a=a^2

and also

(-a)(-a)=a^2

We can notice it doesn't matter the sign of a the square of a is always positive. If we had subtracted in the opposite way, the distance would have resulted in exactly the same. In other words, the above formula is exactly the same as

d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}

As seen, it applies for both coordinates

6 0
2 years ago
Other questions:
  • Keri orders 4 1/2 dozen cupcakes for her graduation party. If each dozen costs $7.28, what is her total bill before tax?
    14·2 answers
  • What is the rule for the function whose graph is shown ?
    8·1 answer
  • Simplify these problems to help me understand on how to do the problems
    13·1 answer
  • What is the answer?
    13·1 answer
  • A point is chosen randomly on JM. Identify the probability that the point is on JK or LM. HELP Please!! I don't understand......
    13·1 answer
  • HELP ME WITH THIS NOW PLS
    9·1 answer
  • Simplify the expression:<br> (1 + 6g)(3) =
    11·1 answer
  • A pound of chocolate costs 8 dollars. Ivan buys p pounds. Write an equation to represent the total cost c that Ivan pays.
    8·1 answer
  • Samantha bought 26 total fish. Each goldfish cost $3 and each guppy costs $4. She spent $86 total. How many guppies did she buy?
    10·1 answer
  • Help immediately!!
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!