document.write( "Question 827182: The combined perimeters of the 2 squares is 52 in. When they are placed together, the third figure is formed. It has an outer perimeter of 42 in. Find the sides. \n" ); document.write( "

Algebra.Com's Answer #498576 by LinnW(1048) $\"\"$ $\"About$

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S = side length of smaller
\n" ); document.write( "L = side length of larger
\n" ); document.write( "4S + 4L = 52
\n" ); document.write( "Now consider the figure where the two squares are set next to each other.
\n" ); document.write( "This figure will have 3 sides of length L, 3 sides of length S
\n" ); document.write( "and additional perimeter where the squares join.
\n" ); document.write( "The area where they join can be represented by L - S
\n" ); document.write( "So the equation for the new figure is
\n" ); document.write( "3L + 3S + L - ( L-S ) = 42 We are subtracting the covered portion.
\n" ); document.write( "3L + 3S + L - L + S = 42
\n" ); document.write( "3L + 4S = 42
\n" ); document.write( "Now we have two equations
\n" ); document.write( "4S + 4L = 52
\n" ); document.write( "4S + 3L = 42
\n" ); document.write( "subtract the bottom from the top
\n" ); document.write( " L = 10
\n" ); document.write( "Substitute L = 10 in 4S + 3L = 42
\n" ); document.write( " 4S + 3(10) = 42
\n" ); document.write( " 4S + 30 = 42
\n" ); document.write( "subtract 30 from each side
\n" ); document.write( " 4S = 12
\n" ); document.write( " S = 4
\n" ); document.write( "So the smaller square is 4 x 4 and the larger 10 x 10
\n" ); document.write( " \n" ); document.write( "

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