ΔABC is right angled at A. AB = 60 units, AC = 80 units and BC = 100 units. D is a point between B and C such that ΔADB and ΔADC have equal perimeters. What is the length of BD?
A
10 units
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B
20 units
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C
40 units
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D
60 units
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Solution
The correct option is D 60 units Let DC=x Then BD=100−x [∵BC=100 units] Perimeter of ΔADB=AD+100−x+60=AD+160−x Perimeter of ΔADC=AD+DC+AC=AD+x+80 According to the given condition, Perimeter of ΔADB= Perimeter of ΔADC ⇒AD+160−x=AD+x+80⇒160−x=x+80⇒80−2x=0⇒x=40. ∴BD=100−x=100−40=60units.