please prove this question
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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・ิ)
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・ิ)
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nobel:
thanks dude
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