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In the diagram below,  D is the midpoint of the base of isosceles triangle ABC. Points  G1 and G2 are the centroids of  ABD and ACD, respectively. We know AD=8 and G1G2 =4. What is the perimeter of ABC?

 Nov 18, 2019
 #1
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From the diagram, BD = DC = G_1 G_2 = 4.  Then from the Pythaogrean Theorem, AB = sqrt(4^2 + 8^2) = 4*sqrt(5), so the peimeter is AB + AC + BC = 4*sqrt(5) + 4*sqrt(5) + 8 = 8*sqrt(5) + 8.

 Nov 18, 2019
 #2
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Actually it was 32.

 Nov 23, 2019

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