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A rectangle has a perimeter of 80 cm and its length is 1 cm more than twice its width. Find the dimensions of a rectangle given that its perimeter is 80 cm and its length is 1 cm more than twice its width. Set up your solution using the variables L for the length, W for the width, and P for the perimeter. Part a: Using the definition of the perimeter, write an equation for P in terms of L and W. Part b: Using the relationship given in the problem statement, write an equation for L in terms of W. Solve the equations from parts a and b. Part c: The length is ? Cm. Part d: The width is? Cm.

Sagot :

Answer: (a) P = 6W + 2

(b) L = 2W + 1

(c) Width = 13cm

Length = 27cm

Step-by-step explanation:

The formula for perimeter of a rectangle is 2(length + width). Since the length is 1 cm more than twice its width, then the length will be:

L = (2 × W) + 1

(b) L = 2W + 1

Therefore, P = 2(L + W)

P = 2( 2W + 1) + 2W

P = 4W + 2 + 2W

(a) P = 6W + 2

Since perimeter is given as 80cm. Therefore,

P = 6W + 2

6W + 2 = 80

6W = 80 - 2

6W = 78

W = 78/6

W = 13

Width is 13cm

Length = 2W + 1

Length = 2(13) + 1

Length = 27cm

The width of the rectangle is 13cm and the length is 27cm.

Description of a rectangle

A rectangle is a quadrilateral. Opposite sides are equal. The four angles in a rectangle is equal to 90 degrees.

The formula for determining the perimeter of a rectangle = 2x (length + width)

P = 2(L + W)

  • Perimeter = 80
  • length = 1 + 2w
  • Width = w

Determining the values of width and length

80 = 2(1 + 2w + w)

80 = 2(1 + 3w)

40 = 1 + 3w

40 - 1 = 3w

39 = 3w

w = 13cm

Length = 1 + 2(13) = 27cm

To learn more about rectangles, please check: https://brainly.com/question/16595449

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