In an equilateral triangle prove that the square of one side is equal to four times the square of one of its altitude.
In an equilateral triangle prove that the square of one side is equal to four times the square of one of its altitude.
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Answer:
Let ABC be equilateral triangle.
Let AD be perpendicular bisector from A on to BC. So BD = CD = 1/2 BC
ADC is a right angle triangle. So AC² = AD² + DC²
AC² = AD² + (1/2 AC)²
AD² = 3/4 AC²
4 AD² = 3 AC²
Answer:
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Step-by-step explanation:
Let a be the side of the equilateral triangle.
∴BE=EC=2BC=2a
To prove:- 4AE2=3a2
In △ABE, by pythagoras theorem
AB2=AE2+BE2
a2=AE2+(2a)2
⇒AE2=a2−4a2
⇒AE2=44a2−a2
⇒AE2=43a2
⇒4AE2=3a2
Hence proved that three times the square of one side is equal to four times the square of one of its altitudes.