Question

in triangle ABC DE is parallel to Bc if AD is equal to 4 Db= 6 and EC= 12 then the value of AE=​

Answer 1

Step-by-step explanation:

ANSWER

REF.Image.

In △ADE and △ABC

∠A=∠A [common]

Since DE∥BC, DB and EC will

act as traversals

∴∠ADE=∠ABC  

and ∠AED=∠ACB [corresponding angles]

So, by similarity of triangles : △ADE∼△ABC[By AAA citiesion]

∴ABAD=ACAE(x+2)+(3x+16)x+2=x+(3x+5)x

(4x+18)(x+2)=(4x+5)x⇒(x+2)(4x+5)=x(4x+18)

⇒4x2+5x+8x+10=4x2+18x⇒5x=10⇒x=2