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, From (1) and (2) $\frac{\mathrm{AB}}{\mathrm{AD}}=\frac{\mathrm{AC}}{\mathrm{AE}}$ In ∆ABC and ∆ADE, $\frac{\mathrm{AB}}{\mathrm{AD}}=\frac{\mathrm{AC}}{\mathrm{AE}}$     (Proved) ∠A = ∠A       (Common) ∴ ∆ABC $~$ ∆ADE    (SAS Similarity) $⇒\frac{\mathrm{AB}}{\mathrm{AD}}=\frac{\mathrm{BC}}{\mathrm{DE}}=\frac{\mathrm{AC}}{\mathrm{AE}}$     (If two triangles are similar, then their corresponding sides are proportional) 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__.MathematicsRD Sharma (2020, 2021)All

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