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Using the diagram on the right, find the length of GT and TA.

Using the diagram on the right, find the length of GT and TA.-example-1
User Tacet
by
8.2k points

1 Answer

3 votes

Answer:


GT=10\ units and
TA=6\ units

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


(GR)/(GE)=(GT)/(GA)

we have


GR=5\ units


GE=5+3=8\ units


GT=16-x\ units


GA=16\ units

substitute


(5)/(8)=(16-x)/(16)\\ \\5*16=8*(16-x)\\ \\80=128-8x\\ \\8x=128-80\\ \\x=48/8\\ \\x=6\ units

therefore


GT=16-x=16-6=10\ units


TA=x=6\ units

User Michelange
by
8.4k points

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