document.write( "Question 855643: The perimeter of two similar triangles have a ratio of 2:4. The sum of the areas of the triangles add up to 100cm^2. What is the area of each triangle? \n" ); document.write( "

Algebra.Com's Answer #515503 by josgarithmetic(39618) $\"\"$ $\"About$

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Perimeter being a length, or a distance, means the side lengths are also in the same 2:4 proportion, actually 1:2 ratio, because 1:2 is reduced.\r
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\n" ); document.write( "\n" ); document.write( "Small triangle:
\n" ); document.write( "perimeter x+y+z, and if assumed z is a hypotenuse and the triangles are Right, then
\n" ); document.write( "area is $\"%281%2F2%29xy\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Large triangle:
\n" ); document.write( "perimeter would be 2x+2y+2z=2(x+y+z). As similar to the small one,
\n" ); document.write( "area is $\"%281%2F2%29%282x%29%282y%29=2xy\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Look at now the ratio of their areas. (1/2):2, or $\"%281%2F2%29%2F2=1%2F4\"$ , small to large; This means, if cut the large AND small together into 5 equal parts, the small triangle is 1 of those parts, and the large triangle is 4 of those parts; together making the 5 equal parts.\r
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\n" ); document.write( "\n" ); document.write( "Cut $\"100cm%5E3\"$ into 5 equal parts: $\"20cm%5E3\"$ in each part. This means small triangle is $\"20cm%5E3\"$ and large triangle is $\"80cm%5E3\"$ . \n" ); document.write( "

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