Question

please prove this question

Answer 1

this is your answer above

mark as brainlist

Answer 2

Geometry,

We have triangle ABC

BE such that BE = (1/4)BC = (1/4)AB ( because equilateral triangle)

Now as in the picture we know that the if one side is k in equilateral triangle the height will be √3/2 k (not showing the calculation),
in here we'll let k as 4BE because 4BE also equal to AB ok,

Now (1/2k²)+(√3/2k)² = k²

=> (1/2 × 4BE)² + (√3/2 × 4BE)²= AB²

=> 1/4 × 16BE² + 3/4 × 16BE² = AB²

=> 4BE² + 12BE² = AB²

=> 16BE² = AB²

=> BE² = AB²/16........(1)

And, (1/4k)² + (√3/2k) = AE²

=> (1/4 × 4BE)²+ (√3/2 × 4BE)² = AE²

=> BE² + 12BE² = AE²

=> 13BE² = AE ²

=> BE² = AE²/13.........(2)

Equating equaltion 1 and 2 we get,

AB²/13 = AE²/16
Now by cross multiplication we get,

=> 16AB² = 13AE² [ proved]

That's it
Hope it helped (･ิω･ิ)