Answer:
[tex]GT=10\ units[/tex] and [tex]TA=6\ units[/tex]
Step-by-step explanation:
we know that
In the diagram
Triangles GRT and GEA are similar by AA Similarity Postulate
Remember that
If two figures are similar, then the ratio of its corresponding sides is proportional
so
[tex]\frac{GR}{GE}=\frac{GT}{GA}[/tex]
we have
[tex]GR=5\ units[/tex]
[tex]GE=5+3=8\ units[/tex]
[tex]GT=16-x\ units[/tex]
[tex]GA=16\ units[/tex]
substitute
[tex]\frac{5}{8}=\frac{16-x}{16}\\ \\5*16=8*(16-x)\\ \\80=128-8x\\ \\8x=128-80\\ \\x=48/8\\ \\x=6\ units[/tex]
therefore
[tex]GT=16-x=16-6=10\ units[/tex]
[tex]TA=x=6\ units[/tex]
