Question

Solve for z please I am not sure need answer ASAP

Answer 1

In Triangle ABD using Pythagoras theorem we can write

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

Now In Triangle BCD Using Pythagoras theorem we get

$BC^2=BD^2+CD^2\\ \\ z^2=7^2+BD^2\\ \\ z^2=49+BD^2$

Now in larger Triangle ABC using Pythagoras theorem we can write

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

Now substitute the values from above two equations we get

$AB^2+z^2=(9+7)^2\\ \\ 81+BD^2+z^2=16^2\\ \\ BD^2=z^2-49\\ \\ 81+z^2-49+z^2=256\\ \\ 2z^2=224\\ \\ z^2=112\\ \\ z=4\sqrt{7}$