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nika2105 [10]
2 years ago
11

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

Mathematics
1 answer:
Art [367]2 years ago
5 0

Answer:

GT=10\ units  and TA=6\ units

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

\frac{GR}{GE}=\frac{GT}{GA}

we have

GR=5\ units

GE=5+3=8\ units

GT=16-x\ units

GA=16\ units

substitute

\frac{5}{8}=\frac{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

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