Question

in the given figure triangle ABC is right angled at C perpendicular to a b prove that triangle ABC similar to triangle and find length of aeand de​

Answer 1

In triangle ΔADE and ΔABC

∠BAC = ∠EAD.............(common angle)

∠AED = ∠ACB.................(each 90 degree)

hence, ΔADE is similar to ΔABC

In ΔABC , ∠C=90°

Therefore, AB²=AC²+BC²...............pythagoras theorem

AB=√5²+12²

    =√25+144

   =√169

   =13 cm

Therefore AB/AD=BC/DE=AC/AE..................ΔABC is similar to ΔADE

⇒13/3=12/DE=5/AE

⇒DE=12×3/13

  =36/13

and AE=5×3/13

    =15/13

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