Question Number 190678 by cortano12 last updated on 08/Apr/23
Answered by som(math1967) last updated on 09/Apr/23
$$\:{x}^{\mathrm{2}} ={AG}^{\mathrm{2}} −{GD}^{\mathrm{2}} \\ $$$$=\mathrm{12}^{\mathrm{2}} +{GE}^{\mathrm{2}} −{GD}^{\mathrm{2}} \\ $$$$=\mathrm{12}^{\mathrm{2}} +{BG}^{\mathrm{2}} −\mathrm{6}^{\mathrm{2}} −{GD}^{\mathrm{2}} \\ $$$$=\mathrm{12}^{\mathrm{2}} −\mathrm{6}^{\mathrm{2}} +\mathrm{8}^{\mathrm{2}} +{GF}^{\mathrm{2}} −{GD}^{\mathrm{2}} \\ $$$$=\mathrm{12}^{\mathrm{2}} +\mathrm{28}+{GC}^{\mathrm{2}} −\mathrm{14}^{\mathrm{2}} −{GD}^{\mathrm{2}} \\ $$$$=\mathrm{28}−\mathrm{52}+\mathrm{13}^{\mathrm{2}} +{GD}^{\mathrm{2}} −{GD}^{\mathrm{2}} \\ $$$$=\mathrm{169}−\mathrm{24} \\ $$$${x}=\sqrt{\mathrm{145}} \\ $$
Commented by som(math1967) last updated on 09/Apr/23
Answered by horsebrand11 last updated on 09/Apr/23
$$\:{x}^{\mathrm{2}} +\mathrm{6}^{\mathrm{2}} +\mathrm{14}^{\mathrm{2}} =\:\mathrm{12}^{\mathrm{2}} +\mathrm{8}^{\mathrm{2}} +\mathrm{13}^{\mathrm{2}} \\ $$$$\:{x}^{\mathrm{2}} +\mathrm{36}+\mathrm{196}=\mathrm{144}+\mathrm{64}+\mathrm{169} \\ $$$$\:{x}=\sqrt{\mathrm{145}}\: \\ $$