In the diagram of ACFE below, GD||FE, CG=10, CD=12, and DE=72. What is the length of CF? С 10 12 G D 72 Do F E Spomit Arcus Answet Type here to search O

Sagot :

In the given triangle FCE and GCD

angle C is common

as line GD || FE

angle EFC = angle DGC (corresponding angle)

Similarly

Angle CDG = AngleCEF (Corresponding angle)

By Angle Angle similarity, triangle FCE and GCD are similar

From thr properties of similar triangle,

The ratio of corresponding sides of similar triangle are equal

[tex]\begin{gathered} In\text{ }\Delta FCE\text{ \&}\Delta\text{ GCD} \\ \frac{FC}{GC}=\frac{CE}{CD}=\frac{EF}{DG} \end{gathered}[/tex]

substitute the value: GC = 10, CD = 12, DE = 72

as: CE = CD + DE

CE = 12 + 72

CE = 84

[tex]\begin{gathered} \frac{FC}{GC}=\frac{CE}{CD}=\frac{EF}{DG} \\ \frac{FC}{10}=\frac{84}{12}=\frac{EF}{DG} \end{gathered}[/tex]

For the length CF, simplify first two expression:

[tex]\begin{gathered} \frac{CF}{10}=\frac{84}{12} \\ CF=\frac{84\times10}{12} \\ CF=7\times10 \\ CF=70 \end{gathered}[/tex]

Answer : CF = 70