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gtnhenbr [62]
3 years ago
8

Given that ABC~LMN What is the length of AC?

Mathematics
1 answer:
sleet_krkn [62]3 years ago
6 0

Answer:

B. 12

Step-by-step explanation:

✔️Find the value of x

The side lengths of two similar triangles are always proportional.

Given that ∆ABC ~ ∆LMN, therefore:

\frac{AB}{LM} = \frac{AC}{LN}

AB = 5

LM = 10

AC = x + 5

LN = 3x + 3

Plug in the values

\frac{5}{10} = \frac{x + 5}{3x + 3}

Cross multiply

5(3x + 3) = 10(x + 5)

15x + 15 = 10x + 50 (distributive property)

Collect like terms

15x - 10x = -15 + 50

5x = 35

Divide both sides by 5

x = 7

✔️Find AC

AC = x + 5

Plug in the value of x

AC = 7 + 5

AC = 12

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If x is the least common multiple of the set {6, 8, 12} and y is the greatest common factor
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Answer:

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Step-by-step explanation:

The least common multiple of {6,8,12} is 24. This can be intuitively figured by noting that any multiple of 12 is a multiple of 6 and that 12 is 1.5x larger than 8. That means we only have so multiple 12 by 2 and 8 by 3 for them to be equal. The GCF of {20,42,72} is 2 as the prime factorization of 20 is 2x2x5 and 42 is 2x3x7. That means even without having to check 72 (which is clearly even so 2 is a factor), we know that 2 is the greatest common factor that they could share. So X/Y = 24/2 = 12

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gizmo_the_mogwai [7]

Answer:

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Explanation:
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So, let us suppose that the measures are, 3k, 7k, 8k.
Evidently, their sum is
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