Question

$\Delta ABC$ 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 $\Delta ADB$ and $\Delta ADC$ have equal perimeters. What is the length of BD?

• A. 10 units
• B. 20 units
• C. 40 units
• D. 60 units

Answer 1

The correct option is D 60 units


Let $DC=x$ Then $BD=100-x$ [$\because BC=100$ units]
Perimeter of $\Delta ADB$ $=AD+100-x+60$ $=AD+160-x$
Perimeter of $\Delta ADC$ $=AD+DC+AC$ $=AD+x+80$
According to the given condition,
Perimeter of $\Delta ADB$= Perimeter of $\Delta ADC$
$\Rightarrow AD+160-x=AD+x+80\Rightarrow 160-x=x+80\Rightarrow 80-2x=0\Rightarrow x=40$.
$\therefore$ $BD=100-x=100-40=60units.$