document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #299189 by ewatrrr(24785) $\"\"$ $\"About$

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document.write( "Hi
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document.write( "Note: 30-60-90 triangle, sides have a ratio 1:sqrt(3):2  
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document.write( "Area[short leg = 8in] = (1/2)*8*8sqrt(3) = 32sqrt(3)
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document.write( "Area[short leg = 24in] = (1/2)*24*24sqrt(3) = 288sqrt(3)
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document.write( "ratio of the areas is 32/288 = 1/9  or 1:9
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document.write( "Why 1:9 because 1:3^2 is 1:9  
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document.write( "larger triangle: shortest leg of that is 3 times the smaller's shortest leg\r
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document.write( "What would be the ratio of the areas of two triangles 
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document.write( "with short legs 5 and 20 inches long?
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document.write( "  1:4^2 or 1:16 \n" );
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