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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?
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`
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