Question

In the diagram below, \overline{FG}
FG
is parallel to \overline{CD}
CD
. If FGFG is 1010 less than FEFE, CE=64CE=64, and CD=48CD=48, find the length of \overline{FE}
FE
. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.

Answer 1

The length of the segment $\overline{FE}$ can be found with the aid of the triangle

proportionality theorem.

The length of $\overline{FE}$ is 40

Reasons:

The given parameters are;

$\overline{FG}$ ║ $\overline{CD}$

$\overline{FG}$ = $\overline{FE}$ - 10

$\overline{CE}$ = 64, $\overline{CD}$ = 48

Required:

To find the length of $\overline{FE}$

Solution:

By triangle proportionality theorem, we have;

$\dfrac{\overline{FE}}{\overline{CE}} = \dfrac{\overline{FG}}{\overline{CD}}$

Therefore;

$\dfrac{\overline{FE}}{{64}} = \dfrac{\overline{FE} - 10}{{48}}$

Which gives;

48 × $\overline{FE}$ = 64 × ($\overline{FE}$ - 10)

64 × $\overline{FE}$ - 48 × $\overline{FE}$ = 64 × 10 = 640

(64 × $\overline{FE}$ - 48 × $\overline{FE}$ =  16 × $\overline{FE}$)

16 × $\overline{FE}$ = 640

$\overline{FE} = \dfrac{640}{16} = 40$

The length of $\overline{FE}$ = 40

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