1. In an equilateral triangle ABC, whose length of each side is 3 cm, D is the point on BC such that BD = ½ CD. What is the length of AD?
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By: anil on 05 May 2019 02.38 am
Given : AB = AC = BC = 3 cm and BD = $$frac{1}{2}$$ CD AE is median. To find : $$AD = ?$$ Solution : BD + CD = 3 => $$BD + 2BD = 3BD = 3$$ => $$BD = frac{3}{3} = 1$$ cm Also, since AE is media => $$BE = CE = frac{3}{2}$$ cm => $$DE = BE - DE = frac{3}{2} - 1 = frac{1}{2}$$ cm Also, AE = $$frac{sqrt{3}}{2} a = frac{3 sqrt{3}}{2}$$ cm In $$ riangle$$ ADE => $$(AD)^2 = (AE)^2 + (DE)^2$$ => $$(AD)^2 = (frac{3 sqrt{3}}{2})^2 + (frac{1}{2})^2$$ => $$(AD)^2 = frac{27}{4} + frac{1}{4} = frac{28}{4}$$ => $$AD = sqrt{7}$$ cm
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