document.write( "Question 914497: The ratio of the areas of 2 squares is 6:7. If the perimeter of the larger square is 73.5 what is the perimeter of the smaller aquare? Please help me solve them. Thank youuuu so much 😊😊😊
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Algebra.Com's Answer #555150 by KMST(5328) $\"\"$ $\"About$

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If the side lengths of the smaller and larger squares are $\"s\"$ and $\"S\"$ respectively,
\n" ); document.write( "the perimeters are $\"4%2As\"$ and $\"4%2AS\"$ respectively,
\n" ); document.write( "with $\"4%2AS=73.5\"$
\n" ); document.write( "The ratio of their sides and perimeters is $\"s%2FS=4%2As%2F4S\"$ ,
\n" ); document.write( "and the ratio of their areas is $\"s%5E2%2FS%5E2\"$ .
\n" ); document.write( "We know that $\"s%5E2%2FS%5E2=6%2F7\"$ .
\n" ); document.write( " $\"s%5E2%2FS%5E2=6%2F7\"$ --> $\"%28s%2FS%29%5E2=6%2F7\"$ --> $\"4%2As%2F4S=sqrt%286%2F7%29\"$ --> $\"4%2As=sqrt%286%2F7%29%2A%284%2AS%29\"$
\n" ); document.write( "So, $\"4%2As=sqrt%286%2F7%29%2A73.5\"$ ---> $\"4%2As=highlight%2868.0%29\"$ (rounded).\r
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\n" ); document.write( "\n" ); document.write( "NOTES:
\n" ); document.write( "In general, when you have similar shapes (same figure, or 3-D solid, but scaled up or down),
\n" ); document.write( "if the ratio of length measures (side lengths, perimeters, circumferences, etc) is $\"R\"$ ,
\n" ); document.write( "then the ratio of the corresponding areas is $\"R%5E2\"$ ,
\n" ); document.write( "and (if the similar shapes are 3-dimensional) the ratio of the volumes is $\"R%5E3\"$ .
\n" ); document.write( "The larger square is a scaled up version of the smaller square, so that applies.
\n" ); document.write( "(We could not say the same of triangles, or rectangles). \n" ); document.write( "

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