Respuesta :

kudzordzifrancis

Answer:

[tex]x=12cm[/tex]

Step-by-step explanation:

Triangle DEF is similar to triangle HGF.

Therefore the corresponding sides are proportional.

We can write the following equations for the corresponding sides.

[tex]\frac{DF}{HF}=\frac{EF}{GF}[/tex]


This implies that,

[tex]\frac{16+40}{40}=\frac{x+30}{30}[/tex]


This gives us,


[tex]\frac{7}{5}=\frac{x+30}{30}[/tex]


We cross multiply to get,

[tex]7\times 30=5(x+30)[/tex]


We divide through by 5 to get,


[tex]7\times 6=(x+30)[/tex]

We multiply to get,

[tex]\Rightarrow 42=x+30[/tex]

Grouping like terms gives,

[tex]\Rightarrow 42-30=x[/tex]

We simplify to obtain,

[tex]\therefore x=12cm[/tex]


The correct answer is C





alinakincsem

Answer:

The value of x is 12 cm.

Step-by-step explanation:

From the given figure, we know that the lines ED and GH are parallel and triangle DEF and triangle FGH are congruent to each other.

Therefore, the corresponding sides of these triangles will also be proportional so we can write it as:

[tex]\frac{GF}{EF} = \frac{FH}{FD}[/tex]

[tex]\frac{30}{30+x} =\frac{40}{40+16}[/tex]

[tex]\frac{30}{30+x} =\frac{40}{56}[/tex]

[tex]1680=1200+40x[/tex]

[tex]40x=1680-1200[/tex]

[tex]x= \frac{480}{40}[/tex]

[tex]x=12[/tex]

Therefore, the value of x is 12 cm.

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