Question

I need help with this Geometry question asap. It's on special triangles.

Answer 1

4√5

Explanation:

the rule is: AB/n=n/BC.

from the rule above n²=AB*BC and AB=sqrt(144-n²).

After substitution n²=10*√(144-n²).

In order to solve this equation:

n⁴=100(144-n²); ⇔ n⁴+100n²-14400=0;

`\left[\begin{array}{ccc}n^2=-180\\\ n^2=80\end{array}\right]  \ => \ \left[\begin{array}{ccc}n=√(-80) \\\ n=√(80) \end{array}\right] \ => \ n=√(80).`

P.S. sqrt{80}=4√5.