Question

What is the value of x in the figure below?15CDBX20A.2015B. 10C. 300D. 5E 20OFF.454

Answer 1

From the image, and using the Pythagorean theorem in ΔABC:

`\begin{gathered} AB^2+AC^2=BC^2 \\ 15^2+AC^2=20^2 \\ 225+AC^2=400 \\ AC^2=175 \\ AC=5√(7) \end{gathered}`

Additionally, we know that:

`\begin{gathered} CD+DB=BC \\ \Rightarrow DB=20-x \end{gathered}`

Finally, using the altitude on hypotenuse theorem:

`\begin{gathered} AC^2=CD\cdot BC \\ 15^2=x\cdot20 \\ \therefore x=(45)/(4) \end{gathered}`