In $△$ ABC, $∠$ C is right angle. D & E are mid points of AC & AB of AB = $10$ & AC = $6$ cm. Find length of DE.

4 c m

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5 c m

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3 c m

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6 c m

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Solution

The correct option is A $4 c m$
The line segment going the mid point of any two sides of a triangle
is parallel to third side and is half of it.
$∴ D E = \frac{1}{2} B C,$
$A C^{2} + B C^{2} = A B^{2}$
$B C = \sqrt{A B^{2} - A C^{2}} = \sqrt{100 - 36}$
$B C = \sqrt{64}, B C = 8$
$D E = \frac{1}{2} B C = \frac{1}{2} (8) = 4 c m$

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In △ ABC, ∠ C is right angle. D & E are mid points of AC & AB of AB = 10 & AC = 6cm. Find length of DE.

The correct option is A 4cmThe line segment going the mid point of any two sides of a triangleis parallel to third side and is half of it.∴DE=12BC,AC2+BC2=AB2BC=√AB2−AC2=√100−36BC=√64,BC=8DE=12BC=12(8)=4cm

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