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svp [43]
2 years ago
7

Triangles ABC and DEF are similar. The ratio of the side lengths in triangle ABC to triangle DEF is 1:3. If the area of triangle

ABC is 1 square unit, what is the area of triangle DEF?
Mathematics
2 answers:
yan [13]2 years ago
8 0
<span>Triangles ABC and DEF are similar. The ratio of the side lengths in triangle ABC to triangle DEF is 1:3. If the area of triangle ABC is 1 square unit, what is the area of triangle DEF?
</span>
Dimas [21]2 years ago
8 0

Answer:

The area of triangle DEF is 9 square units.

Step-by-step explanation:

It is given that triangle ABC and DEF are similar and the ratio of the side lengths in triangle ABC to triangle DEF is 1:3.

Let the length of their sides be x and x respectively.

If two triangles are similar then the ratio of their areas is equal to the square of the ratio of their sides.

Since triangle ABC and DEF are similar, therefore

\frac{Area(ABC)}{Area(DE F)}=\frac{(x)^2}{(3x)^2}

\frac{1}{Area(DE F)}=\frac{(x)^2}{9(x)^2}

Cancel out the common factors.

\frac{1}{Area(DE F)}=\frac{1}{9}

On cross multiplication, we get

1\times 9=1\times Area(DE F)}

9=Area(DE F)}

Therefore the area of triangle DEF is 9 square units.

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tino4ka555 [31]
 If we're talking about a box with dimensions 10 ft, 19 ft and 20 ft, it's probable that the instructions say to calculate the volume.  That would be

V = (10 ft)(19 ft)(20 ft) = 3800 cubic feet.
8 0
3 years ago
A sample of an unknown liquid has a volume of 24.0 mL and a mass of 6 g. What is its density?
Furkat [3]

Answer:

Hey there!

Density = Mass/Volume

Mass= 6g

Volume=24 mL, which is 24 cm^3

Density= 6g/24 cm^3

Density=0.25 g/cm^3

Let me know if this helps :)

5 0
3 years ago
Read 2 more answers
Gwen had an awful time camping! When she got home, she counted 5 mosquito bites on her legs for every 4 bites on her arms. Gwen
pogonyaev

Answer:

5*4 = 20

20 + 3 = 23

answer : 23

Step-by-step explanation:

7 0
2 years ago
One common factor of two numbers is 40. Another common factor is 10. If both numbers are less than 100, what are the two numbers
Viefleur [7K]
Only two numbers less than 100 have a factor of 40: 40 (1 x 40) and 80 (2 x 40). Since 40 is a factor of both 40 and 80, 10 must also be a factor - indeed, 40 = 4 x 10 and 80 = 8 x 10.

The two number must be 40 and 80.
5 0
3 years ago
2. In your own words, explain HOW to find the standard deviation of this data set. (20 points) 3. What does the standard deviati
Ket [755]

Answer:

\sigma = 11.28 --- Standard deviation

Step-by-step explanation:

Given

See attachment for graph

Solving (a): Explain how the standard deviation is calculated.

<u>Start by calculating the mean</u>

To do this, we divide the sum of the products of grade and number of students by the total number of students;

i.e.

\bar x = \frac{\sum fx}{\sum f}

So, we have:

\bar x = \frac{50 * 1 + 57 * 2 + 60 * 4 + 65 * 3 +72 *3 + 75 * 12 + 77 * 10 + 81 * 6 + 83 * 6 + 88 * 9 + 90 * 12 + 92 * 12 +95 * 2 + 99 * 4 + 100 * 5}{1 + 2 + 4 + 3 +3 + 12 + 10 + 6 + 6 + 9 + 12 + 12 +2 + 4 + 5}

\bar x = \frac{7531}{91}

\bar x = 82.76

Next, calculate the variance using the following formula:

\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f}

i.e subtract the mean from each dataset; take the squares; add up the squares; then divide the sum by the number of dataset

So, we have:

\sigma^2 = \frac{1 * (50 - 82.76)^2 +...................+ 5 * (100 - 82.76)^2}{91}

\sigma^2 = \frac{11580.6816}{91}

\sigma^2 = 127.26

Lastly, take the square root of the variance to get the standard deviation

\sigma = \sqrt{\sigma^2}

\sigma = \sqrt{127.26}

\sigma = 11.28 --- approximated

<em>Hence, the standard deviation is approximately 11.28</em>

Considering the calculated mean (i.e. 82.76), the standard deviation (i.e. 11.28) is small and this means that the grade of the students are close to the average grade.

8 0
2 years ago
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