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2 years ago

The perimeters of similar triangles are in the same ratio as the corresponding sides.

Mathematics

2 answers:

Verdich [7]2 years ago

8 0

Answer:

The perimeters of similar triangles are always in the same ratio as the corresponding sides.

Step-by-step explanation:

The perimeter of triangle is sum of all the sides of the triangle.

Let we have two similar triangles with a scale factor s

Therefore, if sides of one triangle are a,b, and c

then the sides of the second triangle are given by : as, bs, and cs

Now, perimeter of first triangle, P = a + b + c

Perimeter of second triangle, Q = sa + sb + sc

⇒ Q = s × (a+ b+ c)

⇒ Q = s × P

Hence, The perimeters of similar triangles are always in the same ratio as the corresponding sides.

Therefore, the correct answer is ALWAYS

const2013 [10]2 years ago

7 0

A. Always is the Answer to this

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2 years ago

Last week’s and this week’s low temperatures are shown in the table below.

zavuch27 [327]

Answer:

1st, 2nd, 3rd and 5th statement are correct choices.

Step-by-step explanation:

We have been given a table of low temperatures during last week and this week. We are asked to choose the correct options from our given choices about the center and variability of data.

Low Temperatures of this Week (f): 4, 10, 6, 9 ,6.

Low Temperatures of the last Week (f): 13, 9, 5, 8, 5.

Let us check our given choices one by one.

1. The mean of this week's temperatures is greater than 5 degrees.

$\text{Mean of the low temperatures this week}=\frac{4+10+6+9+6}{5}$

$\text{Mean of the low temperatures this week}=\frac{35}{5}$

$\text{Mean of the low temperatures this week}=7$

Since the mean of this week's temperatures is 7 and 7 is greater than 5, therefore, 1st statement is true.

2. The mean of last week's temperatures is greater than 5 degrees.

$\text{Mean of the low temperatures last week}=\frac{13+9+5+8+5}{5}$

$\text{Mean of the low temperatures last week}=\frac{40}{5}$

$\text{Mean of the low temperatures last week}=8$

Since the mean of last week’s temperatures is 8 and 8 is greater than 5, therefore, 2nd statement is true as well.

3. The range of this week's temperatures is greater than 5 degrees.

We know that range is the difference between greatest value and smallest value of data set.

$\text{Range}=\text{ Greatest value of data set-Lowest value of data set}$

$\text{Range of the low temperature this week}=10-4$

$\text{Range of the low temperature this week}=6$

We can see that range of low temperature this week is 6 and 6 is greater than 5, therefore, 3rd statement is true.

4. The mode of last week's temperatures is greater than 5 degrees.

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5. The range of last week's temperatures is greater than 5 degrees.

$\text{Range of the low temperature last week}=13-5$

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We can see that range of last week's temperatures is 8 and 8 is greater than 5, therefore, 5th statement is a correct choice.

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