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Question

In ∆ABC, sides AB and AC are extended to D and E respectively, such that AB = BD and AC = CE. If BC = 6 cm, then DE = ___________.


Solution


In ∆ABC, sides AB and AC are extended to D and E, respectively such that AB = BD and AC = CE.



Now,

ABAD=ABAB+BD=ABAB+AB=AB2AB=12    .....1ACAE=ACAC+CE=ACAC+AC=AC2AC=12   .....2

From (1) and (2)

ABAD=ACAE

In ∆ABC and ∆ADE,

ABAD=ACAE     (Proved)

∠A = ∠A       (Common)

∴ ∆ABC ~ ∆ADE    (SAS Similarity)

ABAD=BCDE=ACAE     (If two triangles are similar, then their corresponding sides are proportional)

12=6 cmDEDE=2 × 6=12 cm

In ∆ABC, sides AB and AC are extended to D and E respectively, such that AB = BD and AC = CE. If BC = 6 cm, then DE = __12 cm__.

Mathematics
RD Sharma (2020, 2021)
All

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