Given:
QSR is a right triangle.
QT = 10
TR = 4
To find:
The value of q.
Solution:
Hypotenuse of QSR = QT + TR
= 10 + 4
= 14
Geometric mean of similar right triangle formula:
[tex]$\frac{\text { hypotenuse }}{\text { leg }}=\frac{\text { leg }}{\text { part }}$[/tex]
[tex]$\Rightarrow \frac{14}{q} =\frac{q}{4}[/tex]
Do cross multiplication.
[tex]$\Rightarrow14\times 4 =q\times q[/tex]
[tex]$\Rightarrow 56 =q^2[/tex]
Switch the sides.
[tex]$\Rightarrow q^2 =56[/tex]
Taking square root on both sides.
[tex]\Rightarrow q =2 \sqrt{14}[/tex]
The value of q is [tex]2 \sqrt{14}[/tex].
