Question

Solve for y please I have no clue I am so lost thank you

Answer 1

In the Triangle ABD, Using Pythagoras theorem we can write

$AB^2=BD^2+AD^2\\ \\ AB^2=9^2+y^2\\ \\ AB^2=81+y^2$

In the Triangle ACD using Pythagoras Theorem

$AC^2=AD^2+CD^2\\ \\ AC^2=y^2+7^2\\ \\ AC^2=y^2+49$

Now in the larger Triangle ABC, we can write

$AB^2+AC^2=BC^2$

Now substitute the values from the above equations we get

$81+y^2+49+y^2=(9+7)^2\\ \\ 130+2y^2=16^2\\ \\ 130+2y^2=256\\ \\ 65+y^2=128\\ \\ y^2=128-65=63\\ \\ y=\sqrt{63} =3\sqrt{7}$