the perimeter of a rectangle is 74 feet. the length of the rectangle is 3 feet less than 4 times the width. what is the width of the rectangle in feet?

74= 2l+2w
l=4w-3

Substitute the l value
74= 2(4w-3)+2w
74= 8w-6+2w
74=10w-6
80=10w
8=w

Final answer: 8 ft

To check, find length and plug values in
l= 4w-3
l=4(8)-3
l=32-3
l=29

74=2(29)+2(8)
True
29= 4(8)-3
True

Answer Link

Lanuel Lanuel · Answer 2 · 2021-11-18T10:10:06+01:00

Since the perimeter of this rectangle is 74 feet, the width of the rectangle is 8 feet.

Let the length of the rectangle be L.

Let the width of the rectangle be W.

Given the following data:

Perimeter of rectangle = 74 feet.

Translating the word problem into an algebraic equation, we have;

[tex]L=4W-3[/tex]

To find the width of the rectangle;

Mathematically, the perimeter of a rectangle is given by the formula;

[tex]P = 2(L+W)[/tex]

Substituting the values into the formula, we have;

[tex]74=2(4W-3 +W)\\\\74=2(5W-3)\\\\74=10W-6\\\\10W=74+6\\\\10W=80\\\\W=\frac{80}{10}[/tex]

Width, W = 8 feet.

Therefore, the width of the rectangle is 8 feet.

Find more information: https://brainly.com/question/11037225