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ABC is an equilateral triangle D is a point on BC such that BD=1/3BC then prove that 9AB^2 = 7AD^2

Posted by Indu Mahipal 6 years, 9 months ago

CBSE > Class 10 > Mathematics

2 answers

Ram Kushwah 6 years, 9 months ago

Sorry i can not draw figure here

Just drop perpendicular AE from A to BC

suppose side of triangle is 6x then

AD=2x and DE=x and AB = 3x and BE=3x

so AE²= AB² -BE²

= (6x)²-(3x)² =36x²-9x² =27x²

Now in triangle ADE

AD²=AE² + DE²

=27 x²+ x² = 28 x²

AD²= 28/36 *36x²= 28/36 *AB²= 7/9*AB²

7 AD²= 9 AB²

0Thank You

Indu Mahipal 6 years, 9 months ago

Sorry , show that 9AD^2 = 7AB^²

3Thank You

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