Hi

Note: 30-60-90 triangle, sides have a ratio 1:sqrt(3):2  

Area[short leg = 8in] = (1/2)*8*8sqrt(3) = 32sqrt(3)

Area[short leg = 24in] = (1/2)*24*24sqrt(3) = 288sqrt(3)

ratio of the areas is 32/288 = 1/9  or 1:9

Why 1:9 because 1:3^2 is 1:9  

larger triangle: shortest leg of that is 3 times the smaller's shortest leg



What would be the ratio of the areas of two triangles 

with short legs 5 and 20 inches long?

  1:4^2 or 1:16 

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