# 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? - Mathematics

Sum

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?

#### Solution

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

Concept: Triangles Examples and Solutions
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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 7 Triangles
Q 9 | Page 129