Question

What is the length of segment AE?

(3 points – 1 point correct formula(s), 1 point correct proportion(s), 1 point accurate calculations)

Answer 1

`AE=(50)/(3)\ units`

Explanation:

step 1

In the right triangle ABC

Applying the Pythagoras Theorem fin the hypotenuse AC

`AC^(2) =AB^(2)+BC^(2)`

substitute

`AC^(2) =6^(2)+8^(2)`

`AC^(2) =100`

`AC =10\ units`

step 2

we know that

If two figures are similar, then the ratio of its corresponding sides is equal

so

`(AB)/(CD)=(AC)/(CE)`

substitute and solve for CE

`(6)/(4)=(10)/(CE)\\ \\CE=4*10/6\\ \\CE=(20)/(3)\ units`

step 3

Find the length of segment AE

AE=AC+CE

substitute the values

`AE=10\ units+(20)/(3)\ units=(50)/(3)\ units`