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Question

mathstudent55 · Answer

Sometimes, separating the triangles makes it easier to understand.

mathstudent55 · Answer

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mathstudent55 · Answer

Side BD corresponds to side AE.
The ratio of BD to AE is 3 : 4.
Ok?

mathstudent55 · Answer

Side CD corresponds to side CE.
The length of CD is 5.2.
The length of CE is 5.2 + x.
The ratio of CD to CE is 5.2 : (5.2 + x)

mathstudent55 · Answer

Now you set the two ratios equal. You have an equation in x, and you can solve for x.

$ \dfrac{3}{4} = \dfrac{5.2}{5.2 + x} $

You can cross multiply to solve the equation for x.

mathstudent55 · Answer

$\dfrac{3}{4} = \dfrac{5.2}{5.2 + x}$

$3 ( 5.2 + x) = 4 \cdot 5.2$

$15.6 + 3x = 20.8 $

$3x = 5.2$

$x = \dfrac{5.2}{3} $

$x = 1.7333...$

$x \approx 1.73$