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Triangle DEF is the medial triangle of triangle ABC and triangle XYZ is the medial triangle of triangle DEF. If the perimeter of triangle XYZ is 5, what is the perimeter of triangle ABC?

beastrohit  Nov 28, 2018
 #1
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By a property of medial triangles, each side of the medial triangle will be parallel to one side of its enclosing triangle....and the length of each of the sides of the medial triangle will be (1/2) the length of its respective parallel side....so....this must mean that the perimeter of triangle DEF will be twice that  of the perimeter of  triangle XYZ

 

And ....by like reasoning.....triangle ABC will have twice the perimeter of triangle DEF

 

So....the perimeter of ABC   =    5^(2)^2  =  20 units

 

 

cool cool cool

CPhill  Nov 28, 2018

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