Question and Answers Forum

All Questions      Topic List

Geometry Questions

Previous in All Question      Next in All Question      

Previous in Geometry      Next in Geometry      

Question Number 27055 by Joel578 last updated on 01/Jan/18

Commented by Joel578 last updated on 01/Jan/18

EB = 4 ED = 8 EC = 7 Find EA

$${EB}\:=\:\mathrm{4} \\ $$$${ED}\:=\:\mathrm{8} \\ $$$${EC}\:=\:\mathrm{7} \\ $$$$\mathrm{Find}\:{EA} \\ $$

Answered by mrW1 last updated on 01/Jan/18

Commented by mrW1 last updated on 01/Jan/18

a^2 +c^2 =4^2 ...(i) a^2 +d^2 =8^2 ...(ii) b^2 +d^2 =7^2 ...(iii) (i)+(iii)−(ii): a^2 +c^2 +b^2 +d^2 −a^2 −d^2 =4^2 +7^2 −8^2 c^2 +b^2 =4^2 +7^2 −8^2 =1=x^2 ⇒EA=x=(√1)=1 generally: EA^2 +ED^2 =EB^2 +EC^2

$${a}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{4}^{\mathrm{2}} \:\:\:...\left({i}\right) \\ $$$${a}^{\mathrm{2}} +{d}^{\mathrm{2}} =\mathrm{8}^{\mathrm{2}} \:\:...\left({ii}\right) \\ $$$${b}^{\mathrm{2}} +{d}^{\mathrm{2}} =\mathrm{7}^{\mathrm{2}} \:\:\:...\left({iii}\right) \\ $$$$\left({i}\right)+\left({iii}\right)−\left({ii}\right): \\ $$$${a}^{\mathrm{2}} +{c}^{\mathrm{2}} +{b}^{\mathrm{2}} +{d}^{\mathrm{2}} −{a}^{\mathrm{2}} −{d}^{\mathrm{2}} =\mathrm{4}^{\mathrm{2}} +\mathrm{7}^{\mathrm{2}} −\mathrm{8}^{\mathrm{2}} \\ $$$${c}^{\mathrm{2}} +{b}^{\mathrm{2}} =\mathrm{4}^{\mathrm{2}} +\mathrm{7}^{\mathrm{2}} −\mathrm{8}^{\mathrm{2}} =\mathrm{1}={x}^{\mathrm{2}} \\ $$$$\Rightarrow{EA}={x}=\sqrt{\mathrm{1}}=\mathrm{1} \\ $$$$ \\ $$$${generally}: \\ $$$${EA}^{\mathrm{2}} +{ED}^{\mathrm{2}} ={EB}^{\mathrm{2}} +{EC}^{\mathrm{2}} \\ $$

Commented by Rasheed.Sindhi last updated on 01/Jan/18

Excellent!

$$\mathcal{E}{xcellent}! \\ $$

Commented by Joel578 last updated on 02/Jan/18

thank you very much

$${thank}\:{you}\:{very}\:{much} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com