Question

Find the exact length of EC.

Answer 1

`√(246)`

Explanation:

The scale factor is
`(4√(138) )/(√(138))` = 4

If AB = 6
`√(3)` then AC = 24
`√(3)` 4 times longer.

Using a² + b² = c² substitute a = 4
`√(138)`, b = 24
`√(3)`, and c = DC = x

`(4√(138))^2 + (24√(3) )^2= x^2`

2208 + 1728 = x²

3936 = x²

`√(3936) = x`

4
`\sqrt{246` this is the length of DC

Now the length of EC is 4 times shorter, so EC =
`√(246)`