in the given figure triangle ABC is right angled at C prove that ABC similar to ADE and also find the length of AE and DE
Answers
We need to show that
1- ABC is similar to ADE?
2- find the length of AE
3-find the length of DE?
AB= x
BC= 12
AC= 3+2 = 5
AE= y
ED= z
AD= 3
If both triangles are right angles and they are similar then it can be said that
ABC= AED
y 3 z
----------- = ----------------- = ------------
x 5 12
First lets find value of x, using Pythagoras theorem.
we have two sides available and one is missing, so we can find it.
H²= P²+B²
(x)²= (5)²+(12)²
solve that and you will get that x= 13
Lets take a look at this scenario again:
y 3 z
----------- = ----------------- = ------------
x 5 12
Now we have value of x
y 3 z
----------- = ----------------- = ------------
13 5 12
find value of y
y 3
----------- = -----------------
13 5
cross multiple and value of y= 7.8
3 z
----------------- = -------------------
5 12
cross multiple and you will find that value of z= 7.2