Menu Close

Question-169009




Question Number 169009 by mr W last updated on 23/Apr/22
Commented by mr W last updated on 23/Apr/22
Q168830 reposted with changed value.
$${Q}\mathrm{168830}\:{reposted}\:{with}\:{changed}\:{value}. \\ $$
Commented by infinityaction last updated on 23/Apr/22
Commented by mr W last updated on 23/Apr/22
just think!  m^2 =3×(3+9)=36 ⇒m=6  BD=m=6  ΔPBD has side lengthes 3,6,3.   and you think such a triangle is  possible?  that′s why i have changed to ∣PA∣=7.
$${just}\:{think}! \\ $$$${m}^{\mathrm{2}} =\mathrm{3}×\left(\mathrm{3}+\mathrm{9}\right)=\mathrm{36}\:\Rightarrow{m}=\mathrm{6} \\ $$$${BD}={m}=\mathrm{6} \\ $$$$\Delta{PBD}\:{has}\:{side}\:{lengthes}\:\mathrm{3},\mathrm{6},\mathrm{3}.\: \\ $$$${and}\:{you}\:{think}\:{such}\:{a}\:{triangle}\:{is} \\ $$$${possible}? \\ $$$${that}'{s}\:{why}\:{i}\:{have}\:{changed}\:{to}\:\mid{PA}\mid=\mathrm{7}. \\ $$
Commented by mr W last updated on 23/Apr/22
your method is correct. the question  is wrong.
$${your}\:{method}\:{is}\:{correct}.\:{the}\:{question} \\ $$$${is}\:{wrong}. \\ $$
Commented by infinityaction last updated on 23/Apr/22
but sir 3,6,3 is a possible tringle   because this is a isosceles tringle
$${but}\:{sir}\:\mathrm{3},\mathrm{6},\mathrm{3}\:{is}\:{a}\:{possible}\:{tringle}\: \\ $$$${because}\:{this}\:{is}\:{a}\:{isosceles}\:{tringle} \\ $$
Commented by mr W last updated on 23/Apr/22
can you show me how this trianlge  looks like?  you think 3,8,3 is also an isosceles  triangle?
$${can}\:{you}\:{show}\:{me}\:{how}\:{this}\:{trianlge} \\ $$$${looks}\:{like}? \\ $$$${you}\:{think}\:\mathrm{3},\mathrm{8},\mathrm{3}\:{is}\:{also}\:{an}\:{isosceles} \\ $$$${triangle}? \\ $$
Commented by infinityaction last updated on 23/Apr/22
got it sir thank you  3,8,3 not a tringle  3+3≯8  thank you sir
$${got}\:{it}\:{sir}\:{thank}\:{you} \\ $$$$\mathrm{3},\mathrm{8},\mathrm{3}\:{not}\:{a}\:{tringle} \\ $$$$\mathrm{3}+\mathrm{3}\ngtr\mathrm{8} \\ $$$${thank}\:{you}\:{sir} \\ $$
Commented by mr W last updated on 23/Apr/22
it′s alright!
$${it}'{s}\:{alright}! \\ $$
Commented by ajfour last updated on 23/Apr/22
Commented by mr W last updated on 23/Apr/22
a good man!
$${a}\:{good}\:{man}! \\ $$
Answered by mr W last updated on 23/Apr/22
AD=DB=BE=a  (3/a)=(a/(7+3))   ⇒a^2 =3×(7+3)=30  ((CF+4)/a)=(a/4)  ⇒CF=(a^2 /4)−4=((30)/4)−4=3.5 ✓
$${AD}={DB}={BE}={a} \\ $$$$\frac{\mathrm{3}}{{a}}=\frac{{a}}{\mathrm{7}+\mathrm{3}}\: \\ $$$$\Rightarrow{a}^{\mathrm{2}} =\mathrm{3}×\left(\mathrm{7}+\mathrm{3}\right)=\mathrm{30} \\ $$$$\frac{{CF}+\mathrm{4}}{{a}}=\frac{{a}}{\mathrm{4}} \\ $$$$\Rightarrow{CF}=\frac{{a}^{\mathrm{2}} }{\mathrm{4}}−\mathrm{4}=\frac{\mathrm{30}}{\mathrm{4}}−\mathrm{4}=\mathrm{3}.\mathrm{5}\:\checkmark \\ $$
Commented by Tawa11 last updated on 23/Apr/22
Great sir
$$\mathrm{Great}\:\mathrm{sir} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *