document.write( "Question 282462: How do I solve the story problem that states, \"find the dimensions of a rectangle that has area 10 and a diagonal of length 5. leave your answer in terms of radicals.\" \n" ); document.write( "
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How do I solve the story problem that states, \"find the dimensions of a rectangle that has area 10 and a diagonal of length 5. leave your answer in terms of radicals.\"\r
\n" ); document.write( "\n" ); document.write( "Let L be the length and W the width. Then the area = L*W = 10 and L = 10/W.\r
\n" ); document.write( "\n" ); document.write( "By the Pythagorean Theorem we have for the triangle created by the diagonal:\r
\n" ); document.write( "\n" ); document.write( "W^2 + (10/W)^2 = 5^2\r
\n" ); document.write( "\n" ); document.write( "W^2 + 100/W^2 = 25
\n" ); document.write( "w^4 + 100 = 25W^2
\n" ); document.write( "W^4 - 25W^2 + 100 = 0
\n" ); document.write( "(W^2-20)*(W^2-5) = 0\r
\n" ); document.write( "\n" ); document.write( "W=sqrt(20) = 2*sqrt(5)
\n" ); document.write( " or
\n" ); document.write( "W=sqrt(5) \r
\n" ); document.write( "\n" ); document.write( "Calculate L = 10/W.\r
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