Question

The perimeter of a rectangle is 46 millimeters. The length of the rectangle can be represented by (3x+3), and its width can be represented by (x−4). What are the dimensions of this rectangle in millimeters?

Answer 1

The dimension of this rectangle = 2mm by 21mm

Where 2 mm = Width of the rectangle

21 mm = Length of the rectangle.

Explanation:

The formula for the perimeter of a rectangle = 2(L + W)

= 2L + 2W

The perimeter = 46 mm

L = 3x + 3

W = x - 4

P = 2L + 2W

46mm = 2(3x + 3) + 2(x - 4)

46 = 6x + 6 + 2x - 8

Collect like terms

46 +8 -6 = 6x + 2x

48 = 8x

x = 48/8

x = 6

Since the Length = 3x + 3

= 3(6) + 3

= 18 + 3

= 21mm

Since the Width = x - 4

= 6 - 4

= 2mm

Therefore, the dimension of this rectangle = 2mm by 21mm

Where 2 mm = Width of the rectangle

21 mm = Length of the rectangle.