document.write( "Question 708254: A triangle has sides 7.5, 9 and 10.5. If the shorest side of a similar triangle is 10, what is the perimeter? \n" ); document.write( "

Algebra.Com's Answer #436040 by jsmallt9(3758) $\"\"$ $\"About$

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Similar triangles have corresponding sides that are proportional. This means that the ratios of each pair of corresponding sides are all equal to each other.

\n" ); document.write( "So the ratio of the two shortest sides:
\n" ); document.write( "7.5/10 is equal to the ratio of the two middle length sides and to the ratio of the two longest sides. We can use this to find the other sides of the second triangle:
\n" ); document.write( "For the middle sides:
\n" ); document.write( " $\"7.5%2F10+=+9%2FM\"$ (where \"M\" is the middle side of the second triangle).
\n" ); document.write( "Cross-multiplying we get:
\n" ); document.write( " $\"7.5M+=+90\"$
\n" ); document.write( "Dividing by 7.5:
\n" ); document.write( " $\"M+=+12\"$

\n" ); document.write( "For the longest sides:
\n" ); document.write( " $\"7.5%2F10+=+10.5%2FL\"$ (where \"L\" is the longest side of the second triangle)
\n" ); document.write( "[Note: We could also have used the ratio of the middle sides (now that we know them both):
\n" ); document.write( " $\"9%2F12+=+10.5%2FL\"$ (where \"L\" is the longest side of the second triangle)]
\n" ); document.write( "Cross-multiplying:
\n" ); document.write( " $\"7.5L=+105\"$
\n" ); document.write( "Dividing by 7.5:
\n" ); document.write( " $\"L=14\"$

\n" ); document.write( "Now that we have all three sides of the second triangle we can find its perimeter:
\n" ); document.write( "10 + 12 + 14 = 36 \n" ); document.write( "

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