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Question Number 156335 by cortano last updated on 10/Oct/21

Commented by cortano last updated on 10/Oct/21

find the perimeter ABCD

$$\mathrm{find}\:\mathrm{the}\:\mathrm{perimeter}\:\mathrm{ABCD} \\ $$

Answered by mr W last updated on 10/Oct/21

Commented by mr W last updated on 10/Oct/21

AE^2 =(a+7)^2 +3^2 −2×3×(a+7) cos 60° =a^2 +11a+37 DE^2 =a^2 +4^2 −2×4×a cos 120° =a^2 +4a+16 DA^2 =7^2 =a^2 +11a+37+a^2 +4a+16−(√((a^2 +11a+37)(a^2 +4a+16))) 2a^2 +15a+4=(√((a^2 +11a+37)(a^2 +4a+16))) ... ⇒a=2 perimeter ABCD=2+2×7+9=25

$${AE}^{\mathrm{2}} =\left({a}+\mathrm{7}\right)^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} −\mathrm{2}×\mathrm{3}×\left({a}+\mathrm{7}\right)\:\mathrm{cos}\:\mathrm{60}° \\ $$$$\:\:\:\:\:\:\:\:\:={a}^{\mathrm{2}} +\mathrm{11}{a}+\mathrm{37} \\ $$$${DE}^{\mathrm{2}} ={a}^{\mathrm{2}} +\mathrm{4}^{\mathrm{2}} −\mathrm{2}×\mathrm{4}×{a}\:\mathrm{cos}\:\mathrm{120}° \\ $$$$\:\:\:\:\:\:\:\:\:={a}^{\mathrm{2}} +\mathrm{4}{a}+\mathrm{16} \\ $$$${DA}^{\mathrm{2}} =\mathrm{7}^{\mathrm{2}} ={a}^{\mathrm{2}} +\mathrm{11}{a}+\mathrm{37}+{a}^{\mathrm{2}} +\mathrm{4}{a}+\mathrm{16}−\sqrt{\left({a}^{\mathrm{2}} +\mathrm{11}{a}+\mathrm{37}\right)\left({a}^{\mathrm{2}} +\mathrm{4}{a}+\mathrm{16}\right)} \\ $$$$\mathrm{2}{a}^{\mathrm{2}} +\mathrm{15}{a}+\mathrm{4}=\sqrt{\left({a}^{\mathrm{2}} +\mathrm{11}{a}+\mathrm{37}\right)\left({a}^{\mathrm{2}} +\mathrm{4}{a}+\mathrm{16}\right)} \\ $$$$... \\ $$$$\Rightarrow{a}=\mathrm{2} \\ $$$${perimeter}\:{ABCD}=\mathrm{2}+\mathrm{2}×\mathrm{7}+\mathrm{9}=\mathrm{25} \\ $$

Commented by Tawa11 last updated on 10/Oct/21

great sir

$$\mathrm{great}\:\mathrm{sir} \\ $$

Commented by Tawa11 last updated on 10/Oct/21

Sir, please help on Q156270

$$\mathrm{Sir},\:\mathrm{please}\:\mathrm{help}\:\mathrm{on}\:\:\mathrm{Q156270} \\ $$

Commented by mr W last updated on 10/Oct/21

what are you talking about?

$${what}\:{are}\:{you}\:{talking}\:{about}? \\ $$

Commented by Tawa11 last updated on 10/Oct/21

I mean help me with the question. Q156270

$$\mathrm{I}\:\mathrm{mean}\:\mathrm{help}\:\mathrm{me}\:\mathrm{with}\:\mathrm{the}\:\mathrm{question}.\:\:\:\mathrm{Q156270} \\ $$

Commented by mr W last updated on 10/Oct/21

i don′t know what that question is about. i can′t help you by things which i don′t understand.

$${i}\:{don}'{t}\:{know}\:{what}\:{that}\:{question}\:{is} \\ $$$${about}.\:{i}\:{can}'{t}\:{help}\:{you}\:{by}\:{things}\:{which} \\ $$$${i}\:{don}'{t}\:{understand}. \\ $$

Commented by Tawa11 last updated on 10/Oct/21

Alright. Thanks sir.

$$\mathrm{Alright}.\:\mathrm{Thanks}\:\mathrm{sir}. \\ $$

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