Question

If QR = 13 and PT = 8, find QT.

Answer 1

Since the diagram is symmetric ,

so,

$\begin{gathered} QR=QP \\ QP=13 \end{gathered}$

Considering the triangle PQT is,

Using the pythagoras theorem on triangle PQT,

$\begin{gathered} QP^2=PT^2+QT^2 \\ 13^2=8^2+QT^2 \\ QT^2=13^2-8^2 \\ ^{}QT^2=169-64 \\ QT^2=105 \\ QT=\sqrt[]{105} \\ QT=\text{ 10.24 } \end{gathered}$

Hence, the value of QT is 10.24