Question

In a triangle ABC ; AB BC and CA are x 3x+2 and x+4 units respectively where x in N .Find the lengths of its sides.​

Answer 1

Answer:

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]

∴

AB

AD

=

AC

AE

(x+2)+(3x+16)

x+2

=

x+(3x+5)

x

(4x+18)

(x+2)

=

(4x+5)

x

⇒(x+2)(4x+5)=x(4x+18)

⇒4x

2

+5x+8x+10=4x

2

+18x⇒5x=10⇒

x=2

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