Question

If∆ABC~∆PQR, A(∆ABC)=80,A(∆PQR)=125 then find AB/PQ ​

Answer 1

$\huge\fcolorbox{black}{lime}{AnsweR:}$

ΔABC∼ΔPQR ,

A(ΔABC)=80 ,

A(ΔPQR)=125 ,

According to the theorem of areas of similar triangles ""When two triangles are similar, the ratio of areas of those triangles is equal to the ratio of the square of their corresponding sides'

$\bold{\frac{A(\triangle ABC)}{A(\triangle PQR)} =\frac{AB^2}{PQ^2} }\\\\\bold{\frac{80}{125} =\frac{AB^2}{PQ^2} }\\\\\bold{\frac{16}{25}=\frac{AB^2}{PQ^2} }\\\\\bold{\frac{4^2}{5^2}=\frac{AB^2}{PQ^2}, }\\\\\bold{\frac{AB}{PQ}=\frac{4}{5} }\\\\\bold{So,\:\frac{A(\triangle ABC)}{A(\triangle PQR)}=\frac{80}{125} and\:\frac{AB}{PQ}=\frac{4}{5} }$