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Question
In MBC, DE is drawn parallel to BC. If AD: DB=2:3, DE =6cm and AE =3.6cm, find BC and AC.
Solution
Given : DE = 6 cm , AE = 3.6 cm , `"AD"/"DB" = 2/3` , DE || BC
To find : BC and AC
Sol : In Δ ABC , DE || BC
∴ By BPT `"AD"/"DB" = "AE"/"EC"`
`2/3 = 3.6/"x"`
x = `(3.6 xx 2)/2`
= 1.8 × 3
x = 5.4 = EC
∴ AC = 3.6 + 5.4 = 9 cm
AC = 9 cm
In ΔADE and Δ ABC
∠ ADE = ∠ ABC
Similarly ∠AED = ∠ ACB (corresponding angles)
∴ ΔADE ∼ Δ ABC (AA corollary)
`"AE"/"AC" = "DE"/"BC"` (similar sides of angles)
`3.6/9 = 6 /"y"`
y = `(9 xx 6)/3.6`
y = 15
BC = 15 cm
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