Question

The areas of two similar triangles `Delta ABC` and `Delta PQR ` are `25 cm^(2)` and `49 cm^(2)` respectively. If `QR=9.8` cm, find `BC`.

Answer 1

We know that the ratio or the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
`:. (ar (Delta ABC))/(ar (Delta PQR))=(BC^(2))/(QR^(2))` ltbr `rArr ((BC)/(QR)^(2))= (ar (Delta ABC))/(ar (Delta PQR))=(25)/(49)=((5)/(7))^(2)` ltbr `rArr (BC)/(QR)=(5)/(7)rArr (BC)/(9.8)=(5)/(7)`
`rArr BC(5xx9.8)/(7) cm= 5xx1.4 m= 7 cm`
Hence, BC=7cm