Question

15. In an equilateral triangle ABC, D is a point on side BC such that BD = 3 BC. Prove
9 AD2 =7AB2

Answer 1

Step-by-step explanation:

Given :-

• equilateral triangle ABC,
• D is a point on side BC such that BD = 3

To Find :-

• Prove 9 AD2 =7AB2

Solution :-

BD=1/3 BC , AB=AC=BC

draw AP perpendicular to BC.

now, BP= 1/2 BC AND BD = 1/3 BC

DP=BP-BD

=1/2 BC - 1/3 BC

= 1/6 BC

in triangle APD, 

AD² = AP² + DP²..........(1)

in triangle APB,

AB² = BP² + AP²

AB² = BP²+(AD²-DP²).......FROM (1)

AB² = (1/2 BC)² + AD² - (1/6 BC)²

AB² = 1/4 BC² + AD² - 1/36 BC²

AB² = 1/4 AB² + AD² - 1/36 AB² {AB=BC}

AB² -1/4 AB² + 1/36 AB² = AD²

36 AB² -12 AB² +AB² = 36 AD²

28 AB² = 36 AD²

7 AB² = 9 AD²

Hence proved

Answer 2

Answer:

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