Question

triangle ABC is right angled at C. DE is perpendicular to AB, where D is a point on AC and E is a point on AB. If BC=12cm, AD=3cm and DC=2cm, then prove that triangle ABC is similar to triangle ADE and hence find the lengths of AE and DE.

Answer 1

Please check the image

Answer 2

Ans

Step-by-step explanation:

In triangle ABC and ADE

/_A =/_A ( common)

/_D=/_E ( 90*)

BY AA criteria , ABC ~ ADE

NOW,

AC^2 + BC^2= AB^2

(5)^2 + (12)^2= AB^2

25+144= AB^2

169= AB^2

AB =13

AC/AE =AB/AD = BC/ED

5/AE= 13/3= 12/ED

AE=13/15

ED = 36/13

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(For ATMIYANS)