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Question
In Δ XYZ, XY = 4 cm, YZ = 6 cm, XZ = 5 cm, If ΔXYZ ~ ΔPQR and PQ = 8 cm then find the lengths of remaining sides of ΔPQR.
Solution
Consider, ΔXYZ ~ ΔPQR
`therefore ("XY")/("PQ") = ("YZ")/("QR") = ("XZ")/("PR")` ...[Corresponding sides of similar triangles]
⇒ `4/8 = 6/("QR") = 5/("PR")`
⇒ `4/8 = 6/("QR")`
⇒ `"QR" = (8 xx6)/4`
⇒ QR = 12 cm
⇒ `4/8 = 5/("PR")`
⇒ PR = `(8 xx5)/4`
⇒ PR = 10 cm
Hence, the lengths of remaining sides of ΔPQR are 12 and 10 cm.
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