Math, asked by sanaz, 1 year ago

Prove 9ad square is equal to 7ab square

Answers

Answered by Rishi213
27

 in eq triangle ABC, BD bisects BC such that BD = 1/3 of BC

9AD2  = 7AB2 

 Draw AE ⊥ BC.

In a ΔABC and ΔACE

AB = AC ( Given)

AE = AE ( common)

∠AEB = ∠AEC = 90°

∴ ΔABC ≅ ΔACE ( For RHS criterion)

BE = EC (By C.P.C.T)

BE = EC = BC / 2

In a right angled triangle ADE

AD2 = AE2 + DE2 ---------(1)

In a right angled triangle ABE

AB2 = AE2 + BE2 ---------(2)

From equ (1) and (2) we obtain

⇒ AD2  - AB2 =  DE- BE.

⇒ AD2  - AB2 = (BE – BD)- BE.

⇒ AD2  - AB2 = (BC / 2 – BC/3)– (BC/2)

⇒ AD2  - AB2 = ((3BC – 2BC)/6)– (BC/2)

⇒ AD2  - AB2 = BC/ 36 – BC/ 4 ( In a equilateral triangle ΔABC, AB = BC = CA)

⇒ AD= AB2 + AB/ 36 – AB/ 4

⇒ AD= (36AB2 + AB2– 9AB2) / 36

⇒ AD= (28AB2) / 36

⇒ AD= (7AB2) / 9

9AD= 7AB.





sanaz: tq!!
Answered by garimaa410
0

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