Question

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

Answer 1

It is given that ΔABC ~ ΔPQR

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 = (4.5xx4.5xx16)/9` 

⇒  `QR = sqrt(((4.5xx4.5xx16))/9` 

`= (4.5xx4)/3` 

= 6 cm 

Hence, QR = 6 cm