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

1 Answer
May 24, 2018

10sqrt2

Explanation:

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