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if the triangles are similar, then all the corresponding sides are proportional by the same ratio as one of the sides.
\n" ); document.write( "this means that the ratio of sides of the bigger triangle to the smaler triangle is equal to 15/10 = 1.5.
\n" ); document.write( "this applies to all corresponding parts, including the height.
\n" ); document.write( "the area of the triangle is equal to 1/2 * base * height.
\n" ); document.write( "that would be the area of the smaller triangle.
\n" ); document.write( "the area of the bigger triangle would be equal to 1/2 * 1.5 * base * 1.5 * height which would make the area of the bigger triangle equal to 1.125 * base * height.
\n" ); document.write( "the ration of the area of the bigger triangle to the smaller triangle would therefore be equal to 1.125 * base * height / .5 * base * height which makes the ratio of the areas equal to 1.125 / .5 = 2.25.
\n" ); document.write( "1.5 * 1.5 is equal to 2.25
\n" ); document.write( "this means that the ratio of the area is equal to the ratio of the sides squared.
\n" ); document.write( "this just happens to be the formula that is generally applicable.
\n" ); document.write( "in a 2 dimensional figures, the ratio of the area of similar figures is equal to the ratio of the sides squared.
\n" ); document.write( "in a 3 dimensional figure, the ratio of the volume of similar figures is equal to the ratio of the sides cubed.
\n" ); document.write( "here's a reference:
\n" ); document.write( "http://www.regentsprep.org/Regents/math/geometry/GP11/LMoresimilar.htm
\n" ); document.write( "in your figure the ratio of the sides was 15:10 which i simplified to 1.5 of 1.5:1
\n" ); document.write( "the ratio of the areas is therefore 15^2/100^2 which is equal to 225/100 which i simplified to 2.25.\r
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