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the length of a rectangle is 1 cm more than four times the width. If the perimeter of the rectangle is 22 cm, what are its dimensions

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Answer:

Width = 2 cm; Length = 9 cm

Explanation:

Formula for the perimeter of a rectangle:

The formula for the perimeter of a rectangle is given by:

P = 2L + 2W, where

  • P is the perimeter,
  • L is the length,
  • and W is the width.

Equation relating the rectangle's width and length:

Since the rectangle's length is 1 cm more than four times its width, we can represent this with the following equation:

L = 4W + 1

Finding the width:

Since the rectangles perimeter is 22 cm, we can find its width by substituting 22 for P and 4W + 1 for L in the rectangle perimeter formula:

22 = 2(4W + 1) + 2W

22 = 8W + 2 + 2W

(22 = 10W + 2) - 2

(20 = 10W) / 10

2 = W

Thus, the rectangle's width is 2 cm.

Finding the length:

Now we can find the length by adding 1 to four times the width (2 cm):

L = 4(2) + 1

L = 8 + 1

L = 9

Thus, the length is 9 cm.

User Niko Sams
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