In the $Δ A B C, ∠ B$ is a right angle, $D$ and $E$ are the mid-points of the sides $A B = 3 c m$ and $A C = 5 c m$ respectively. Then, the length of $D E$ is

4 cm

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2 cm

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5 cm

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3 cm

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Solution

The correct option is B 2 cm
In $△ A B C$

$A C^{2} = A B^{2} + B C^{2}$ [Pythagoras theorem]
$\Rightarrow B C^{2} = (5)^{2} - (3)^{2}$
$\Rightarrow B C^{2} = 25 - 9$
$\Rightarrow B C^{2} = 16$
$\Rightarrow B C = 4 c m$
Now,
$D E = \frac{1}{2} B C$ [Mid-point theorem]
$= \frac{1}{2} \times 4 = 2 c m$
Hence, the length of $D E$ is $2 c m$

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In the ΔABC,∠B is a right angle, D and E are the mid-points of the sides AB=3 cm and AC=5 cm respectively. Then, the length of DE is

The correct option is B 2 cmIn △ABC AC2=AB2+BC2 [Pythagoras theorem] ⇒BC2=(5)2−(3)2 ⇒BC2=25−9 ⇒BC2=16 ⇒BC=4 cm Now, DE=12BC [Mid-point theorem] =12×4=2 cm Hence, the length of DE is 2 cm

In the $Δ A B C, ∠ B$ is a right angle, $D$ and $E$ are the mid-points of the sides $A B = 3 c m$ and $A C = 5 c m$ respectively. Then, the length of $D E$ is