Question

In an equilateral triangleABC, E is any point on BC such that BE = 1/4 BC. Prove that 16 AE2 = 13 AB2​

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Secondary School Math 5 points

In an equilateral triangle ABC , E is any point on BC such that BE equals 1/4 BC.prove that 16 AE square is equal to 13 AB square

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jefrinjohnjenny

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sonabrainly Genius

Answer:

oin A to mid-point of BC at D. Hence ED = BE = (1/4)BC --(1)

In triangle AED, AE² = AD² + ED² -----------------(2)

In triangle ABD, AD² = AB² - BD² --------------(3)

Putting value of AD² from (3) into (2),

AE² = AB² - BD² + ED² = AB² - (BC/2)² + (BC/4)²

as BD = (1/2)BC and ED = (1/4)BC from (1).

OR AE² = AB² - (AB/2)² + (AB/4)² as BC = AB as triangle ABC is equilateral.

Simplifying this , 16AE² = 13AB²