Question Number 67692 by mr W last updated on 30/Aug/19
Answered by mr W last updated on 30/Aug/19
Commented by mr W last updated on 30/Aug/19
$${AD}=\sqrt{\mathrm{7}^{\mathrm{2}} +\mathrm{24}^{\mathrm{2}} }=\mathrm{25} \\ $$$${FC}=\sqrt{\mathrm{25}^{\mathrm{2}} −\mathrm{15}^{\mathrm{2}} }=\mathrm{20} \\ $$$$\frac{{HC}}{{FC}}=\frac{{FC}}{{BC}} \\ $$$$\Rightarrow{HC}=\frac{\mathrm{20}^{\mathrm{2}} }{\mathrm{25}}=\mathrm{16} \\ $$$$\frac{{HF}}{{HC}}=\frac{{BF}}{{FC}} \\ $$$$\Rightarrow{HF}=\frac{\mathrm{16}×\mathrm{15}}{\mathrm{20}}=\mathrm{12} \\ $$$$\frac{{FG}}{{GD}}=\frac{{AE}}{{ED}} \\ $$$$\Rightarrow{FG}=\frac{\mathrm{16}×\mathrm{7}}{\mathrm{24}}=\frac{\mathrm{14}}{\mathrm{3}} \\ $$$${AB}={HF}+{FG}=\mathrm{12}+\frac{\mathrm{14}}{\mathrm{3}}=\frac{\mathrm{50}}{\mathrm{3}} \\ $$
Commented by Prithwish sen last updated on 30/Aug/19
$$\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{HF}×\mathrm{BC}=\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{BF}×\mathrm{FC} \\ $$$$\Rightarrow\mathrm{HF}=\:\frac{\mathrm{15}×\mathrm{20}}{\mathrm{25}}\:=\:\mathrm{12} \\ $$
Commented by Prithwish sen last updated on 30/Aug/19
$$\mathrm{Beautiful} \\ $$
Commented by TawaTawa last updated on 30/Aug/19
$$\mathrm{Wow}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$
Commented by behi83417@gmail.com last updated on 30/Aug/19
$$\mathrm{FD}=\mathrm{24}\:\:\mathrm{or}\:\:\mathrm{ED}=\mathrm{24}\:\:? \\ $$$$\mathrm{can}\:\mathrm{it}\:\mathrm{be}\:\mathrm{solved}\:\mathrm{if}:\:\:\mathrm{FD}=\mathrm{24}\:\:? \\ $$
Commented by mr W last updated on 30/Aug/19
$${ED}=\mathrm{24}. \\ $$