Question Number 139840 by mnjuly1970 last updated on 01/May/21
Commented by mnjuly1970 last updated on 01/May/21
$${please}\:{prove}::\Uparrow\Uparrow\Uparrow \\ $$
Answered by mr W last updated on 01/May/21
Commented by mr W last updated on 01/May/21
$${red}\:{shaded}\:{triangles}\:{are}\:{similar}, \\ $$$$\Rightarrow\frac{{p}}{{a}}=\frac{{b}}{{q}} \\ $$$$\Rightarrow{ab}={pq} \\ $$$${green}\:{shaded}\:{triangle}\:{are}\:{similar}, \\ $$$$\Rightarrow\frac{{m}}{{a}}=\frac{{b}}{{n}} \\ $$$$\Rightarrow{ab}={mn} \\ $$$$ \\ $$$$\Rightarrow{ab}={pq}={mn} \\ $$$$\Rightarrow\sqrt{{ab}}=\sqrt{{pq}}=\sqrt{{mn}} \\ $$