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mojhsa [17]
3 years ago
13

Find the length of MG. EGF~EML

Mathematics
1 answer:
elena-14-01-66 [18.8K]3 years ago
8 0

Answer:

The length of MG = 56.

Step-by-step explanation:

Two triangles are similar if their corresponding angles are congruent and corresponding sides are proportional.

Given that: \triangle EGF \sim \triangle EML

From the given figure:

In \triangle EGF and \trinagle EML

EG = 5x+2

EF = 126

EM = 16

EL = 28

By definition of similar triangle,

\frac{EG}{EM}=\frac{EF}{EL}                                                           ...... (1)

Substitute the given values in equation (1) as shown below:

\frac{5x+2}{16}=\frac{126}{28}

5x+2 = 4.5\times 16

5x+2 =72

which implies, EG = 72.

Now to find the value of MG.

EG = EM+MG

72=16+MG

Subtract 16 from both sides, we get

MG = 56

Hence, the value of length of MG = 56.

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Lucia knows the fourth term in a sequence is 55 and the ninth term in the same sequence is 90. Explain how she can find the comm
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Using the formula for the nth term of an arithmetic progression.
an = a + (n - 1)d
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a(9) - a(4) => 5d = 35
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From a(4): a = 55 - 3d = 55 - 3(7) = 55 - 21 = 34

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Step-by-step explanation:

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