Question

PLEASE HELP 45 POINTS!!!!!

Answer 1

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

Answer 2

Answer:

• $\sf x = 5$

• $\sf DF = 12$

setting up proportionality equation:

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

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

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

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

$\sf \hookrightarrow 92 + 4x = 112$

$\sf \hookrightarrow 4x = 112- 92$

$\sf \hookrightarrow 4x = 20$

$\sf \hookrightarrow x = 5$

Find DF:

$\hookrightarrow \sf x + 7$

$\hookrightarrow \sf 5 + 7$

$\hookrightarrow \sf 12$