Question

ABC is a right angle triangle right angled at C. DE perpendicular AB .if BC=12CM ,AD=3cm anD DC =2CM ,then prove that triangle ABC SIMILAR triangle DEF . also find AE AND DE

Answer 1

Answer is in the picture..

Answer 2

Answer:

DE = 36/13cm and AE = 15/13cm

Step-by-step explanation

Given ΔACB is right angled triangle and ∠C = 90 degree

We need to prove that ΔABC∼ΔADE and find the length of AE and DE.

∠A = ∠A (common angle)

∠C = ∠E (Both angles are equal to 90 degree)

So, by AA similarity criterion,we have ΔABC∼ΔADE

Since, AB^2 = AC^2 + BC^2

= 52 + 122

= 132

AB =13

In ΔABC∼ΔADE

AB/AD=BC/DE=AC/AE

13/3=12/DE=5/AE

DE = 36/13cm and AE = 15/13cm