Question and Answers Forum

All Questions      Topic List

Mensuration Questions

Previous in All Question      Next in All Question      

Previous in Mensuration      Next in Mensuration      

Question Number 156184 by cortano last updated on 09/Oct/21

Commented by cortano last updated on 09/Oct/21

base=12, height=9  find radius

$$\mathrm{base}=\mathrm{12},\:\mathrm{height}=\mathrm{9} \\ $$$$\mathrm{find}\:\mathrm{radius} \\ $$

Answered by mr W last updated on 09/Oct/21

Commented by mr W last updated on 09/Oct/21

hypotenuse AC=(√(9^2 +12^2 ))=15 inch  ⇒ΔPQR∼ΔACB  PR=(9/(15))×2r=((6r)/5)  PQ=((12)/(15))×2r=((8r)/5)  AF=AD=9−((6r)/5)−r=9−((11r)/5)  CG=CE=12−((8r)/5)−r=12−((13r)/5)  AC=AF+FG+GC          =9−((11r)/5)+2r+12−((13r)/5)=15  ((14r)/5)=6  r=((15)/7)  ⇒circle diameter=2r=((30)/7) inch

$${hypotenuse}\:{AC}=\sqrt{\mathrm{9}^{\mathrm{2}} +\mathrm{12}^{\mathrm{2}} }=\mathrm{15}\:{inch} \\ $$$$\Rightarrow\Delta{PQR}\sim\Delta{ACB} \\ $$$${PR}=\frac{\mathrm{9}}{\mathrm{15}}×\mathrm{2}{r}=\frac{\mathrm{6}{r}}{\mathrm{5}} \\ $$$${PQ}=\frac{\mathrm{12}}{\mathrm{15}}×\mathrm{2}{r}=\frac{\mathrm{8}{r}}{\mathrm{5}} \\ $$$${AF}={AD}=\mathrm{9}−\frac{\mathrm{6}{r}}{\mathrm{5}}−{r}=\mathrm{9}−\frac{\mathrm{11}{r}}{\mathrm{5}} \\ $$$${CG}={CE}=\mathrm{12}−\frac{\mathrm{8}{r}}{\mathrm{5}}−{r}=\mathrm{12}−\frac{\mathrm{13}{r}}{\mathrm{5}} \\ $$$${AC}={AF}+{FG}+{GC} \\ $$$$\:\:\:\:\:\:\:\:=\mathrm{9}−\frac{\mathrm{11}{r}}{\mathrm{5}}+\mathrm{2}{r}+\mathrm{12}−\frac{\mathrm{13}{r}}{\mathrm{5}}=\mathrm{15} \\ $$$$\frac{\mathrm{14}{r}}{\mathrm{5}}=\mathrm{6} \\ $$$${r}=\frac{\mathrm{15}}{\mathrm{7}} \\ $$$$\Rightarrow{circle}\:{diameter}=\mathrm{2}{r}=\frac{\mathrm{30}}{\mathrm{7}}\:{inch} \\ $$

Commented by cortano last updated on 09/Oct/21

((PR)/(AB))=((PQ)/(AC)) ; ((RQ)/(BC))=((PQ)/(BC))

$$\frac{\mathrm{PR}}{\mathrm{AB}}=\frac{\mathrm{PQ}}{\mathrm{AC}}\:;\:\frac{\mathrm{RQ}}{\mathrm{BC}}=\frac{\mathrm{PQ}}{\mathrm{BC}} \\ $$

Commented by Tawa11 last updated on 10/Oct/21

great sir

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

Answered by nikif99 last updated on 09/Oct/21

Terms of Service

Privacy Policy

Contact: info@tinkutara.com