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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

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Step-by-step explanation:

3(3x + 5) = 2(2x - 5)

9x + 15 = 4x - 10

9x - 4x = -15 - 10

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How would you do these questions?
Delvig [45]

Part 1

Population = {1,2,4}

Sample 1 = {1,1}, probablity = 1/9

Sample 2 = {1,2}, probablity = 1/9

Sample 3 = {1,4}, probablity = 1/9

Sample 4 = {2,1}, probablity = 1/9

Sample 5 = {2,2}, probablity = 1/9

Sample 6 = {2,4}, probablity = 1/9

Sample 7 = {4,1}, probablity = 1/9

Sample 8 = {4,2}, probablity = 1/9

Sample 9 = {4,4}, probablity = 1/9

Each of the 9 samples has equal probablity of occuring, so that's why each probablity is 1/9

Note: it may be best to write the above in the form of a table

==================================================

Part 2

For each sample (1 through 9), compute the mean. So we'll add up the values and divide by 2

xbar represents the sample mean

Sample 1 = {1,1}, xbar = 1

Sample 2 = {1,2}, xbar = 1.5

Sample 3 = {1,4}, xbar = 2.5

Sample 4 = {2,1}, xbar = 1.5

Sample 5 = {2,2}, xbar = 2

Sample 6 = {2,4}, xbar = 3

Sample 7 = {4,1}, xbar = 2.5

Sample 8 = {4,2}, xbar = 3

Sample 9 = {4,4}, xbar = 4

----------

Now let's list out each possible xbar value and its associated probability

xbar = 1, probability = 1/9

xbar = 1.5, probability = 2/9

xbar = 2, probability = 1/9

xbar = 2.5, probability = 2/9

xbar = 3, probability = 2/9

xbar = 4, probability = 1/9

note how the probabilities listed above add to 9/9 = 1.

Again a table is ideal to help organize the data.

==================================================

Part 3

To calculate the value of mu_x, we add up all the xbar values found in part 2, and divide by 9

(1+1.5+2.5+1.5+2+3+2.5+3+4)/9 = 2.333

So mu_x = 2.333 approximately

----------

Calculating the standard deviation is a bit lengthier, but you subtract each data value from the mean, square each difference, and add up the squares.

Afterward, you divide by n = 9 to get the population variance. Apply the square root to get the population standard deviation.

Luckily a calculator or spreadsheet can make quick work of this. You should get roughly 0.88192 as the standard deviation.

==================================================

Part 4

The mean of the population {1,2,4} is (1+2+4)/3 = 2.3333 which matches with mu_xbar

The standard deviation of the population {1,2,4} is roughly 0.88191710368819 which matches with 0.88192 found earlier back in part 3.

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Pls help for geometry
Alex787 [66]

Answer:20

Step-by-step explana

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3 years ago
Please help in this question. I WILL mark brainliest. NO LINKS
deff fn [24]

Answer:

B, you are correct

Area of the bigger trapezoid = (6 + 2) x 1/2 x 6 = 8 x 1/2 x 6 = 4 x 6 = 24

Area of the smaller trapezoid = (4 + 2) x 1/2 x 3 = 6 x 1/2 x 3 = 3 x 3 = 9

<h2>Area of the shaded area = 24 - 9 = 15</h2>

<em>Hope that helps! :)</em>

<em>Hope that helps! :)</em>

<em></em>

<em>-Aphrodite</em>

Step-by-step explanation:

6 0
3 years ago
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