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Licemer1 [7]
2 years ago
10

PLEASE HELP 45 POINTS!!!!!

Mathematics
2 answers:
Andru [333]2 years ago
7 0

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.

\frac{BE+EC}{DF+FC} =\frac{EC}{FC}

\frac{3+4}{(x+7)+16} =\frac{4}{16}

Cross multiply and solve for x.

(3+4)*16=((x+7)+16)*4

7*16=(x+23)*4

112=(x+23)*4

28= (x+23)

x= 5

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

DF=(x+7)

DF=(5+7)

DF= 12

Nady [450]2 years ago
4 0

Answer:

  • \sf x = 5
  • \sf DF = 12

setting up proportionality equation:

\sf \dfrac{big-side}{big-diagonal}   = \sf \dfrac{small-side}{small-diagonal}

\sf \hookrightarrow \dfrac{7}{16+x+7}  = \dfrac{4}{16}

\sf \hookrightarrow  \dfrac{7}{23+x}  = \dfrac{4}{16}

\sf \hookrightarrow 4(23+x) = 112

\sf \hookrightarrow 92 + 4x = 112

\sf \hookrightarrow 4x = 112- 92

\sf \hookrightarrow 4x = 20

\sf \hookrightarrow x = 5

<u>Find DF:</u>

\hookrightarrow \sf x + 7

\hookrightarrow \sf  5 + 7

\hookrightarrow \sf 12

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