Respuesta :

fieryanswererft

Answer:

  • [tex]\sf x = 5[/tex]
  • [tex]\sf DF = 12[/tex]

setting up proportionality equation:

[tex]\sf \dfrac{big-side}{big-diagonal} = \sf \dfrac{small-side}{small-diagonal}[/tex]

[tex]\sf \hookrightarrow \dfrac{7}{16+x+7} = \dfrac{4}{16}[/tex]

[tex]\sf \hookrightarrow \dfrac{7}{23+x} = \dfrac{4}{16}[/tex]

[tex]\sf \hookrightarrow 4(23+x) = 112[/tex]

[tex]\sf \hookrightarrow 92 + 4x = 112[/tex]

[tex]\sf \hookrightarrow 4x = 112- 92[/tex]

[tex]\sf \hookrightarrow 4x = 20[/tex]

[tex]\sf \hookrightarrow x = 5[/tex]

Find DF:

[tex]\hookrightarrow \sf x + 7[/tex]

[tex]\hookrightarrow \sf 5 + 7[/tex]

[tex]\hookrightarrow \sf 12[/tex]

annie413

Answer:

We see 2 congruent triangles: Triangle DBC and FEC. Let's set up a proportion to find the value of x and length of DF.

[tex]\frac{BE+EC}{DF+FC} =\frac{EC}{FC}[/tex]

[tex]\frac{3+4}{(x+7)+16} =\frac{4}{16}[/tex]

Cross multiply and solve for x.

[tex](3+4)*16=((x+7)+16)*4[/tex]

[tex]7*16=(x+23)*4[/tex]

[tex]112=(x+23)*4[/tex]

[tex]28= (x+23)[/tex]

x= 5

Now to solve for the length of DF, plug in x into DF.

DF=(x+7)

DF=(5+7)

DF= 12

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