Question

The areas of two similar triangles ABC and PQR are in the ratio 9:16. If BC = 4.5cm, find the length of QR. 

Answer 1

It is given that Δ ABC ~ Δ PQR
Therefore, the ration of the areas of triangles will be equal to the ratio of squares of their corresponding sides.  

`(ar(ΔABC))/(ar(ΔPQR))=(BC^2)/(QR^2)` 

⇒` 9/16=4^2/(QR^2)` 

⇒` QR^2=(4.5xx4.55xx16)/9` 

⇒  `QR= (sqrt(4.5xx4.5xx16))/9` 

`= (4.5xx4)/3` 

= 6 cm 

Hence, QR = 6 cm