Question

If the areas of two similar triangles ABC and PQR are in the ratio 9 : 16 and BC = 4.5 cm, what is the length of QR?

Answer 1

Given:  ΔABC and ΔPQR are similar triangles. Area of ΔABC: Area of ΔPQR = 9:16 and BC = 4.5cm.

To find: Length of QR

We know that the ratio of the areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides.

Hence,

`(ar(Δ ABC))/(ar(ΔPQR))=(BC^2)/(QR^2)`

`9/16=4.5^2/(QR^2)`

`9/12=4.5^2/(QR^2)`

`QR^2= (4.5^2xx16)/(9)`

`QR^2=36`

`QR= 6 cm`