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
Gnom [1K]
3 years ago
9

The areas of two similar triangles are 18 cm2 and 8 cm2. One of the sides of the first triangle is 4.5 cm. What is the length of

the corresponding side of the other triangle?
Mathematics
2 answers:
muminat3 years ago
3 0

\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\[2em] \begin{array}{ccccllll} &\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\ \cline{2-4}&\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array} \\\\---------------------------------

\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{large}{small}\qquad \qquad \cfrac{side^2}{side^2}=\cfrac{area}{area}\implies \cfrac{4.5^2}{s^2}=\cfrac{18}{8}\implies \cfrac{4.5^2}{s^2}=\cfrac{9}{4}


\bf \left( \cfrac{4.5}{s} \right)^2=\cfrac{3^2}{2^2}\implies \cfrac{4.5}{s}=\sqrt{\cfrac{3^2}{2^2}}\implies \cfrac{4.5}{s}=\cfrac{3}{2}\implies 9=3s \\\\\\ \cfrac{9}{3}=s\implies 3=s

Anettt [7]3 years ago
3 0

Answer:

The corresponding side is 3 cm

Step-by-step explanation:

When we have area, it is the related to the scale factor by the scale factor squared

Area large/ area of small = 18/8 = 9/4

Take the square root

sqrt(9/4)  = 3/2

The scale factor is 3/2    large to small

The large side is 4.5 cm

large         3            4.5 cm

--------   =  ------ =  -----------

small           2           x cm

Using cross products

3x = 2(4.5)

3x =9

Divide each side by 3

3x/3 = 9/3

x =3

You might be interested in
A number is randomly selected from {15, 16, 17, 18, 19, 20}. A is represented by the event that the number picked is less than o
Tatiana [17]
1/3
 the denonator is 6 because that is the number of numbers there are, and the numerator is 2 because there are 2 numbers less than or equal to 16. you can simplify
5 0
3 years ago
Read 2 more answers
Find the reciprocal for each fraction below.
kifflom [539]

Answer:

0.8

Step-by-step explanation:

6 0
3 years ago
Simplify -7x - (15y) + 3x - 2y
LUCKY_DIMON [66]

Answer:

Step-by-step explanation:

combine like terms

-7x + 3x - 15y - 2y

-4x - 17y

3 0
3 years ago
‘z’ is subtracted from (-12) express the expression​
Gnoma [55]

Answer:

Z + 12

Step-by-step explanation:

Z-(-12)

Z + 12

Double negative turns into positive

8 0
3 years ago
What is (x-2)(x+2) in standard from
trasher [3.6K]
Answer= x^2-4

I hope this helps.
5 0
2 years ago
Other questions:
  • Find the area of the circle.
    5·1 answer
  • 3. At the Art Studio 3/8 were red and
    12·2 answers
  • Which statement about the slope of the line is true?
    13·1 answer
  • You have $700 to buy a new carpet for you bedroom write an inequality that represents the cost c per 14 squares for your new car
    9·1 answer
  • A warehouse distributor of carpet faces a normally distributed demand for its carpet. The average demand for carpet from the sto
    10·1 answer
  • A triangle has two sides of length 9 and 6. What is the smallest possible whole-number length for the third side?
    8·2 answers
  • What is the purpose of learning polynomials?
    5·1 answer
  • Pls help!!!
    5·1 answer
  • Draw the image of △abc under a dilation whose center is a and scale factor is 1/4
    12·1 answer
  • 100 POINTS AND BRAINLY
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!