Length of the rectangle = 120 feet
Given :
The width of a rectangle is 3/4 its length. The perimeter of the rectangle is 420 feet.
Let 'L' be the length of the rectangle
Width of the rectangle is 3/4 of its length
width = [tex]\frac{3}{4} \cdot length[/tex]
Perimeter of rectangle = 2(length ) +2(width )
[tex]P=2L+2W\\P=2L+2(\frac{3}{4}\cdot L) \\P=2L+(\frac{3}{2}t L) \\\\P=\frac{7}{2}L \\[/tex]
Given that perimeter of rectangle is 420 feet
Replace perimeter by 420 feet and solve for L
[tex]420= \frac{7}{2} L\\840=7L\\Divide \; by \; 7\\L=120[/tex]
Length of the rectangle = 120 feet
Width of the rectangle =[tex]\frac{3}{4} \cdot length= \frac{3}{4} \cdot 120=90[/tex]
Width of the rectangle = 90 feet
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