Answer:
Therefore,
[tex]v=9\ meter[/tex]
Step-by-step explanation:
Given:
GF = 12
GE = 16
DF = 12
CF = v
To Find:
v = ?
Solution:
In Δ GFC and Δ GED
∠ E ≅ ∠ F …………..{ measure of each angle is 90° given }
∠ G ≅ ∠ G ……….....{Reflexive Property}
Δ GFC ~ Δ GED ….{Angle-Angle Similarity test}
If two triangles are similar then their sides are in proportion.
[tex]\frac{GF}{GE} =\frac{FC}{ED} =\frac{GC}{GD}\ \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]
On substituting the given values we get
[tex]\frac{12}{16} =\frac{v}{12}\\\\v=\frac{144}{16}=9\\\\\therefore v=9\ meter[/tex]
Therefore,
[tex]v=9\ meter[/tex]
