Question

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

Answer 1

`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`