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2 years ago

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

Mathematics

1 answer:

wariber [46]2 years ago

3 0

Answer:

Always

Step-by-step explanation:

Suppose you have triangle ABC with side lengths a, b, c. Suppose that is similar to triangle DEF with side lengths d, e, f.

Now, let k be the ratio of corresponding sides ...

k = d/a

Because the same factor applies to all sides, we also have ...

k = e/b = f/c

That is, if we multiply by the denominators of each of these fractions, we get ...

d = a·k
e =b·k
f = c·k

The perimeter of ΔABC is ...

perimeter(ABC) = a + b + c

The perimeter of ΔDEF is ...

perimeter(DEF) = d + e + f = a·k + b·k + c·k

perimeter(DEF) = k(a + b + c) = k·perimeter(ABC)

k = perimeter(DEF)/perimeter(ABC)

That is, the perimeters are in the same ratio as corresponding sides.

You might be interested in

Solve for x: 6 over x equals 4 over 8

Talja [164]

Answer:

For the given expression, x = 12.

Step-by-step explanation:

Here, in the given expression:

6 over x equals 4 over 8.

Now, 6 over x = $\frac{6}{x}$

and 4 over 8 = $\frac{4}{8}$

So, here $\frac{6}{x} =\frac{4}{8}\\ \implies x = \frac{6 \times 8}{4} = 12$

⇒ x = 12

Hence, for the given expression, x = 12.

5 0

3 years ago

Help me with this Please.

sukhopar [10]

35
the ratio for the two is 5:7 and you want to find _:49. to get from 7 to 49 you multiply the 7 by 7. because you did that to one side you have to do the same to the other and multiply 5 by 7 which gives you 35

6 0

2 years ago

All the items on the sale rack were 75 percent off their original price.

tresset_1 [31]

Answer:

112 $ is the original price

Step-by-step explanation:

$x \times 0.75 = 84 \\ x = 84 \div 0.75 \\ x = 112$

you have to think that the original price multiplied by 0.75 (also known as 75%) gave the result of what he saves i.e 84 $. So we put up an equation with the original price multiplied by 75% which equals the 84 $ he saved on buying that item on sale

4 0

3 years ago

A 13 L solution that was 12% vinegar was mixed with a 9 L solution that was 70% vinegar. What is the concentration of the new mi

erastovalidia [21]

Answer:

The concentration is simply 36%

Step-by-step explanation:

In this question, we are concerned with calculating the concentration of a new mixture formed from mixing some liters of each of two vinegar variants of different concentrations.

We proceed as follows;

The concentration of the new solution will contain 12% of 13L vinegar A and 70% of 9L vinegar B

13L of vinegar A will contain 13 * 12% = 13 * 0.12 = 1.56

9L of 70% vinegar B will contain 9 * 70% = 9 * 0.7 = 6.3

Now, the new mixture has a total volume of 13 + 9 = 22L

The concentration of the new mixture will thus be;

(1.56 + 6.3)/22

= 0.357 and that’s approximately 0.36 or simply 36%

6 0

3 years ago

Kameryn types 75 words per minute and is just starting to write a term paper. Joe already has 510 words written and types at a s

AnnZ [28]

Answer:

Kameryn will have more words typed than Joe when the number of minutes exceeds 34.

Step-by-step explanation:

Let

x -----> the number of minutes

y ----> the total words typed

we know that

<em>Kameryn</em>

$y=75x$ -----> equation A

$y=60x+510$ -----> equation B

Solve the system of equations by substitution

Substitute equation A in equation B and solve for x

$75x=60x+510$

$75x-60x=510$

$15x=510$

$x=34\ minutes$

That means

For x=34 minutes

The amount of words written by Kameryn and Joe are the same.

therefore

For x > 34 minutes

Kameryn will have more words typed than Joe when the number of minutes exceeds 34.

6 0

3 years ago