Question

In Δ XYZ, XY = 4 cm, YZ = 6 cm, XZ = 5 cm, If ΔXYZ ~ Δ​PQR and PQ = 8 cm then find the lengths of remaining sides of ΔPQR.

Answer 1

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.