SOLUTION: If one 30 - 60 - 90 triangle has a short leg 8 inches long, and another has a short leg 24 inches long, find the areas of each triangle, and compare their sizes. Why do you think t

Algebra ->  Length-and-distance -> SOLUTION: If one 30 - 60 - 90 triangle has a short leg 8 inches long, and another has a short leg 24 inches long, find the areas of each triangle, and compare their sizes. Why do you think t      Log On


   

Question 430942: If one 30 - 60 - 90 triangle has a short leg 8 inches long, and another has a short leg 24 inches long, find the areas of each triangle, and compare their sizes. Why do you think the areas have the ratio that they do? What would that ratio be if the two triangles had short legs 5 and 20 inches long?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

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