Question

If DB = 4 and DC = 6, find AD.

2
2
3

Answer 1

`AD =2 (2)/(3)`

EXPLANATION

According the Altitude Theorem, the height of the triangle is equal to the geometric mean of the two segment it creates on the hypotenuse.

This implies that:

`{4}^(2) =6 AD`

`16 = 6 AD`

Divide both sides by 6.

`AD = (16)/(6)`

Simplify

`AD = (8)/(3)`

Change to mixed numbers

`AD =2 (2)/(3)`

Answer 2

B 2 2/3

Explanation:

Triangles ADB and CDB are similar. Therefore similar parts can form a proportion.

AD/DB = DB/DC

AD = ?

DB = 4

DC = 6

x/4 = 4/6 Cross multiply

6x = 16

6x/6 = 16/6

x = 2 4/6 or x = 2 2/3

It's B