Question

a rectangle has length 1/2x+5 and width 1/4x+4. if the perimeter is 42 meters, what are the length and the width of the rectangle.

Answer 1

A rectangle has 2 lengths and 2 widths that equal the perimeter.

`(2)( (1)/(2x) +5)+(2)( (1)/(4x)+4)=42 \\ ((2)( (1)/(2x) +5)+(2)( (1)/(4x)+4))/(2) = (42)/(2) \\ (1)/(2x)+ 5+ (1)/(4x) +4=21 \\ (1)/(2x)+ (1)/(4x) = 12 \\ ( (1)/(x) )( (1)/(2) + (1)/(4) )=12 \\ ( (1)/(x) )( (3)/(4) )=12 \\ (1)/(x) =16 \\ x= (1)/(6) \\ \\ Length: (1)/(2x)+5 \\ (1)/(2( (1)/(16)) )+5 \\ 8+5=13 \\ \\ Width: (1)/(4x)+4 \\ (1)/(4( (1)/(16)) ) +4 \\ 4+4=8`