Answer :
A rectangle has 2 lengths and 2 widths that equal the perimeter.
[tex](2)( \frac{1}{2x} +5)+(2)( \frac{1}{4x}+4)=42 \\ \frac{(2)( \frac{1}{2x} +5)+(2)( \frac{1}{4x}+4)}{2} = \frac{42}{2} \\ \frac{1}{2x}+ 5+ \frac{1}{4x} +4=21 \\ \frac{1}{2x}+ \frac{1}{4x} = 12 \\ ( \frac{1}{x} )( \frac{1}{2} + \frac{1}{4} )=12 \\ ( \frac{1}{x} )( \frac{3}{4} )=12 \\ \frac{1}{x} =16 \\ x= \frac{1}{6} \\ \\ Length: \frac{1}{2x}+5 \\ \frac{1}{2( \frac{1}{16}) }+5 \\ 8+5=13 \\ \\ Width: \frac{1}{4x}+4 \\ \frac{1}{4( \frac{1}{16}) } +4 \\ 4+4=8 [/tex]
[tex](2)( \frac{1}{2x} +5)+(2)( \frac{1}{4x}+4)=42 \\ \frac{(2)( \frac{1}{2x} +5)+(2)( \frac{1}{4x}+4)}{2} = \frac{42}{2} \\ \frac{1}{2x}+ 5+ \frac{1}{4x} +4=21 \\ \frac{1}{2x}+ \frac{1}{4x} = 12 \\ ( \frac{1}{x} )( \frac{1}{2} + \frac{1}{4} )=12 \\ ( \frac{1}{x} )( \frac{3}{4} )=12 \\ \frac{1}{x} =16 \\ x= \frac{1}{6} \\ \\ Length: \frac{1}{2x}+5 \\ \frac{1}{2( \frac{1}{16}) }+5 \\ 8+5=13 \\ \\ Width: \frac{1}{4x}+4 \\ \frac{1}{4( \frac{1}{16}) } +4 \\ 4+4=8 [/tex]
