Question

In given figure,$\angle DFE={90}^0,FL\perp ED,LD=8,FL=12,$ find
1. $EL$
2. $FD$
3. $EF$

Answer 1

In $△DLF$ & $△DFE$,

$\angle D=\angle D$ [same angle]

$\angle DLF=\angle DFE$ [Both ${90}^{\circ }$]

$\angle DFL=\angle DEF$ [Remaining angles]

Now, $\frac{DL}{DF}=\frac{DF}{DE}=\frac{FL}{FE}$

Now, $144+64=D{F}^2$

$\frac{82}{\sqrt{208}}=\frac{12}{FE}$

$\Rightarrow FE=\frac{3\sqrt{208}}{2}=\frac{3\sqrt{4\times 4\times 13}}{2}$

$E{L}^2+F{L}^2=E{F}^2$

$\Rightarrow E{L}^2=36\times 13-144$

$\Rightarrow EL=18$

$\therefore EL=18,EF=6\sqrt{1}3,FD=4\sqrt{1}3$