InterviewSolution
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InterviewSolution
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In a Δ ABC , AD is the bisector of ∠A, meeting side BC at D. (i) If BD = 2.5 cm, AB = 5 cm and AV = 4.2 cm, find DC. (ii) If BD = 2 cm, AB = 5 cm and DC = 3 cm, find AC. (iii) If AB = 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD. (iv) If AB = 10 cm, AC = 14 cm and BC = 6 cm, find BD and DC. (v) If AC = 4.2 cm, DC = 6 cm and BC = 10 cm, find AB. (vi) If AB = 5.6 cm, AC = 6 cm and DC = 6 cm, find BC. (vii) If AD = 5.6 cm, BC = 6 cm and BD = 3.2 cm, find AC. (viii) If AB = 10 cm, AC = 6 cm and BC = 12 cm, find BD and DC. |
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Answer» (i) we have Angle BAD=CAD Here AD bisects ∠A BD/DC=AB/AC 2.5/DC=5/4.2 DC=2.5 x 4.2/5 DC=2.1 cm (ii) Here AD bisects ∠A AB/DC=AB/AC 2/3=5/AC AC=15/2 AC=7.5 cm (iii) in △ ABC A bisects ∠A BD/DC = AB/BC BD/2.8 = 3.5/4.2 BD =3.5 x 2.8/4.2 BD = 7/3 BD = 2.33 cm (iv) In△ABC, AD bisects ∠A BD/DC = AB/AC X/6 - x = 10/14 14x = 60 - 10x 14x + 10x = 60 24x = 60 x = 60/24 x = 5/2 x = 2.5 BD = 2.5 DC = 6-2.5 DC = 3.5 (v) AB/AC=BD/DC AB/4.2 = BC - DC/DC AB/4.2 = 10-6/6 AB/4.2 = 4/6 AB = 4 x 4.2/6 AB = 2.8 cm (vi) BD/DC=AB/AC BD/6 = 5.6/6 BD = 5.6 BC = BD + DC BC = 5.6 + 6 BC = 11.6 cm (viii) In△ABC, AD bisects ∠A AB/AC = BD/DC 5.6/AC = 3.2/BC - BD 5.6/AC = 3.2/6 - 3.2 5.6/AC = 3.2/2.8 AC x 3.2 = 2.8 x 5.6 AC = 2.8 x 5.6/3.2 AC = 7 x 0.7 AC = 4.9 cm (ix) let BD =x,then DC=12 - X BD/DC = AB/BC x/12-x = 10/6 6x =120 - 10x 6x + 10x = 120 16x = 120 x = 120/16 x = 7.5 BD = 7.5 cm DC = 12 - x DC =12 - 7.5 DC = 4.5 cm |
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