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Question Number 190678 by cortano12 last updated on 08/Apr/23

Answered by som(math1967) last updated on 09/Apr/23

x^2 =AG^2 −GD^2 =12^2 +GE^2 −GD^2 =12^2 +BG^2 −6^2 −GD^2 =12^2 −6^2 +8^2 +GF^2 −GD^2 =12^2 +28+GC^2 −14^2 −GD^2 =28−52+13^2 +GD^2 −GD^2 =169−24 x=(√(145))

$$\:{x}^{\mathrm{2}} ={AG}^{\mathrm{2}} −{GD}^{\mathrm{2}} \\ $$$$=\mathrm{12}^{\mathrm{2}} +{GE}^{\mathrm{2}} −{GD}^{\mathrm{2}} \\ $$$$=\mathrm{12}^{\mathrm{2}} +{BG}^{\mathrm{2}} −\mathrm{6}^{\mathrm{2}} −{GD}^{\mathrm{2}} \\ $$$$=\mathrm{12}^{\mathrm{2}} −\mathrm{6}^{\mathrm{2}} +\mathrm{8}^{\mathrm{2}} +{GF}^{\mathrm{2}} −{GD}^{\mathrm{2}} \\ $$$$=\mathrm{12}^{\mathrm{2}} +\mathrm{28}+{GC}^{\mathrm{2}} −\mathrm{14}^{\mathrm{2}} −{GD}^{\mathrm{2}} \\ $$$$=\mathrm{28}−\mathrm{52}+\mathrm{13}^{\mathrm{2}} +{GD}^{\mathrm{2}} −{GD}^{\mathrm{2}} \\ $$$$=\mathrm{169}−\mathrm{24} \\ $$$${x}=\sqrt{\mathrm{145}} \\ $$

Commented by som(math1967) last updated on 09/Apr/23

Answered by horsebrand11 last updated on 09/Apr/23

x^2 +6^2 +14^2 = 12^2 +8^2 +13^2 x^2 +36+196=144+64+169 x=(√(145))

$$\:{x}^{\mathrm{2}} +\mathrm{6}^{\mathrm{2}} +\mathrm{14}^{\mathrm{2}} =\:\mathrm{12}^{\mathrm{2}} +\mathrm{8}^{\mathrm{2}} +\mathrm{13}^{\mathrm{2}} \\ $$$$\:{x}^{\mathrm{2}} +\mathrm{36}+\mathrm{196}=\mathrm{144}+\mathrm{64}+\mathrm{169} \\ $$$$\:{x}=\sqrt{\mathrm{145}}\: \\ $$

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