Question

In triangle ABC , D and E are the midpoints of AB and AC.If AD=3.5cm and AE =4cm and DE=2.5cm ,find the perimeter of triangle ABC​

Answer 1

Step by step explanation

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Answer 2

Given : ABC is a triangle , D and E are the mid points of AB and AC.

AD = 3.5 cm

AE = 4 cm

DE = 2.5 cm

To find : Perimeter of Δ ABC= ?

Solution :

Since D and E are the midpoints of AB and AC resp.

So, AD = DB = 3.5 cm

So, $AB=AD+DB=3.5\times 2=7\ cm$

And, AE = EC = 4 cm

So, $AC=AE+EC=2\times 4=8\ cm$

And DE is the half of BC.

So, it becomes :

$DE=\dfrac{1}{2}BC\\\\2.5=\dfrac{1}{2}BC\\\\2\times 2.5=BC\\\\5\ cm=BC$

So, Perimeter of Δ ABC is given by :

$AB+BC+CA=7+8+5=15+5=20\ cm$

Hence, the perimeter is 20 cm.