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Question

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
20 units
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B
10 units
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C
60 units
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D
40 units
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Solution

The correct option is C 60 units

Let DC=x Then BD=100x [BC=100 units]
Perimeter of ΔADB =AD+100x+60 =AD+160x
Perimeter of ΔADC =AD+DC+AC =AD+x+80
According to the given condition,
Perimeter of ΔADB= Perimeter of ΔADC
AD+160x=AD+x+80160x=x+80802x=0x=40.
BD=100x=10040=60 units.

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