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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?

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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
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