An equilateral triangle has sides of 20. What are the lengths of another equilateral triangle with half the area?

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Answer 1 · 2018-05-24T16:10:14

#10sqrt2#

Area of triangle# =1/2a b sinC#

for this equilateral triangle

#A_1=1/2xx20xx20xxsin60#

#A_1=100sqrt3#

now we have the relation

#"ratio of areas " =(" ratio of lengths ")^2#

let the second triangle have area

#A_2#

#A_2=1/2xx100sqrt3=50sqrt3#

so #A_2:A_1::(l_2:20)^2#

#:. (50sqrt3)/(100sqrt3)=l_2^2/400#

#=>l_2^2=1/2xx400#

#l_2=sqrt(200)#

#l_2=10sqrt2#