$△ A B C$ is right angled at $A . A B = 60 c m, A C = 80 c m$ and $B C = 100 c m$ . D is a point between B and C such that $△ A D B$ and $△ A D C$ have equal perimeters. What is the length of $B D$ ?

10 c m

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20 c m

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40 c m

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60 c m

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Solution

The correct option is C $60 c m$
As perimeter of $Δ A D C =$ perimeter of $Δ A D B$

Let length of AD be $^{'} l^{'}$ then,

$l + x + 80 = 60 + l + (100 - x)$

$\Rightarrow 20 = 100 - 2 x \Rightarrow x = 40 c m$

$∴$ length of $B D = (100 - x) = 60 c m$

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△ABC is right angled at A.AB=60 cm,AC=80 cm and BC=100 cm. D is a point between B and C such that △ADB and △ADC have equal perimeters. What is the length of BD?

The correct option is C 60 cmAs perimeter of ΔADC= perimeter of ΔADBLet length of AD be ′l′ then,l+x+80=60+l+(100−x)⇒20=100−2x⇒x=40cm∴ length of BD=(100−x)=60cm

$△ A B C$ is right angled at $A . A B = 60 c m, A C = 80 c m$ and $B C = 100 c m$ . D is a point between B and C such that $△ A D B$ and $△ A D C$ have equal perimeters. What is the length of $B D$ ?

The correct option is C $60 c m$
As perimeter of $Δ A D C =$ perimeter of $Δ A D B$

Let length of AD be $^{'} l^{'}$ then,

$l + x + 80 = 60 + l + (100 - x)$

$\Rightarrow 20 = 100 - 2 x \Rightarrow x = 40 c m$

$∴$ length of $B D = (100 - x) = 60 c m$