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Question
Δ ABC is similar to Δ PQR. If AB = 6cm, BC = 9cm, PQ = 9cm and PR = 10.5cm, find the lengths of AC and QR.
Solution
Given : Δ ABC ∼ Δ PQR
To find : AC and QR
Sol : Δ ABC ∼ Δ PQR
`therefore "AB"/"PQ" = "BC"/"QR" = "AC"/"PR"` (Similar sides of similar triangles)
`6/9 = 9/"y" = "x"/10.5`
`6/9 = 9/"y"` `6/9 = "x"/10.5`
⇒ 6y = 81 ⇒ 63 = 9x
⇒ y = `81/6` ⇒ x = 7
⇒ y = `27/2` ⇒ AC = 7 cm
⇒ QR = 13.5 cm
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