D and E are the points on the sides AB and AC respectively of a ΔABC such that AD = 8 cm, DB = 12 cm, AE = 6 cm and CE = 9 cm. Prove that BC = 5/2 DE.
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Given : AD = 8 cm,DB= 12 cm, AE = 6 cm, and CE = 9cm.
AB = AD + DB = 8 + 12 = 20 cm.
AB = 20 cm.
AC = AE + EC .
AC = 6 + 9 = 15 cm.
AC = 15 cm.
In ΔADE & ΔABC.
AD/AB = 8/20 = 2/5.
AE/AC = 6/15 = 2/5.
AD/AB = AE/AC = 2/5.
∠A = ∠A.
[Common].
ΔADE∼ΔABC (By SAS similarity).
AD/AB = DE/BC .
[Since, corresponding sides of two similar triangles are proportional].
8/20 = DE/BC.
⅖ = DE/BC.
2BC = 5DE.
BC = 5/2DE.
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