Answer:
x = 10.2 units
Step-by-step explanation:
By Geometric mean property:
[tex]BP = \sqrt{AP \times CP} \\ = \sqrt{5 \times 8} \\ BP = \sqrt{40} \\ In \: \triangle BPC\\
BC^2 = BP^2 + PC^2 \\ \therefore \: {x}^{2} = {( \sqrt{40} )}^{2} + ( {8})^{2} \\ \therefore \: {x}^{2} = 40 + 64 \\ \therefore \: {x}^{2} =104 \\ \therefore \: {x} = \sqrt{104} \\ \therefore \: {x} = 10.198039 \\ \huge \red{ \boxed{\therefore \: {x} = 10.2 \: units}}[/tex]
