Question

What is the value of x in the figure below? Show your work.

Answer 1

x = 10.2 units

Explanation:

By Geometric mean property:

`BP = √(AP * CP) \\ = √(5 * 8) \\ BP = √(40) \\ In \: \triangle BPC\\</p><p>BC^2 = BP^2 + PC^2 \\ \therefore \: {x}^(2) = {( √(40) )}^(2) + ( {8})^(2) \\ \therefore \: {x}^(2) = 40 + 64 \\ \therefore \: {x}^(2) =104 \\ \therefore \: {x} = √(104) \\ \therefore \: {x} = 10.198039 \\ \huge \red{ \boxed{\therefore \: {x} = 10.2 \: units}}`