- 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 - ADB and - ADC have equal perimeters- What is the length of BD-

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Δ ABC is righ...

Question

$Δ A B C$ 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 $Δ A D B$ and $Δ A D C$ have equal perimeters. What is the length of BD?

20 units

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10 units

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60 units

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40 units

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Solution

The correct option is C 60 units

Let $D C = x$ Then $B D = 100 - x$ [ $∵ B C = 100$ units]
Perimeter of $Δ A D B$ $= A D + 100 - x + 60$ $= A D + 160 - x$
Perimeter of $Δ A D C$ $= A D + D C + A C$ $= A D + x + 80$
According to the given condition,
Perimeter of $Δ A D B$ = Perimeter of $Δ A D C$
$\Rightarrow A D + 160 - x = A D + x + 80 \Rightarrow 160 - x = x + 80 \Rightarrow 80 - 2 x = 0 \Rightarrow x = 40$ .
$∴$ $B D = 100 - x = 100 - 40 = 60 u n i t s .$

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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?

$Δ A B C$ 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 $Δ A D B$ and $Δ A D C$ have equal perimeters. What is the length of BD?