Question

in an equilateral triangle ABC,D is a point on side BC such that BD=1/3BC. prove that 9AD²=7AB²​

Answer 1

$\huge\fcolorbox{black}{aqua}{Solution:-}$

✏️ ɢıvεŋ :-

★ ศŋ εզนıɭศtεгศɭ ∆ศ๖ɕ, шɧεгε ɖ ıร ศ ℘σıŋt σŋ tɧε รıɖε ๖ɕ รนɕɧ tɧศt ๖ɕ = ๖ɖ/3 σг ๖ɖ = 1/3 × ๖ɕ.

✏️ tσ ℘гσvε :-

★ 9(ศɖ)² = 7(ศ๖)²

✏️ ɕσŋรtгนɕtıσŋ :-

★ ɖгศш ศε ⊥ ๖ɕ.

✏️ ℘гσσʄ :-

★ ∵ ศε ⊥ ๖ɕ,

⇒∆ศε๖ ≅ ∆ศεɕ

[๖ყ гɧร ɕσŋɢгนεŋɕყ ɕгıtεгıσŋ]

∴ ๖ε = εɕ = ½ ๖ɕ = ½ ศ๖

ɭεt, ศ๖ = ๖ɕ = ศɕ = χ

ŋσш,

๖ε = χ/2 ศŋɖ

ɖε = ๖ε - ๖ɖ

⇒ɖε = χ/2 - χ/3

⇒ɖε = χ/6

ŋσш,

นรıŋɢ tɧε ℘ყtɧศɢσгศร tɧεσгεɱ, шε ɧศvε,

ศ๖² = ศε² + ๖ε² ....→ (1)

ศŋɖ

ศɖ² = ศε² + ɖε² ....→ (2)

tɧนร,

ʄгσɱ (1) ศŋɖ (2), шε ɢεt,

ศ๖² - ศɖ² = ๖ε² - ɖε²

⇒χ² - ศɖ² = [χ/2]² - [χ/6]²

⇒ศɖ² = χ² - χ²/4 + χ²/36

⇒ศɖ² = 28/36 χ²

⇒9ศɖ² = 7ศ๖² .

ɧεŋɕε ℘гσvεɖ!

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Answer 2

Answer:

Check your answer please