The length of a rectangle is 3 centimeters more than 3 times the width. If the perimeter of the rectangle is 46 centimeters, find the dimensions of the rectangle.
Let the width of the rectangle be x cm.
The length is then 3x + 3 cm.
The perimeter is given by the formula: P = 2(l + w)
Substituting the given values, we get 46 = 2((3x + 3) + x)
Simplifying the right side of the equation, we get 46 = 2(4x + 3)
Multiplying through the brackets, we get 46 = 8x + 6
Subtracting 6 from both sides, we get 40 = 8x
Dividing through by 8, we get x = 5 cm
The width of the rectangle is 5 cm, and the length is 3(5) + 3 = 18 cm. Answer: \boxed{5, 18}.
To solve this problem, let's represent the width of the rectangle as "w" centimeters.
According to the given information, the length of the rectangle is 3 centimeters more than 3 times the width. So, the length can be expressed as 3w + 3 centimeters.
The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, it is given that the perimeter of the rectangle is 46 centimeters.
The formula to calculate the perimeter of a rectangle is:
Perimeter = 2 * (Length + Width)
Substituting the given values into the formula, we have:
46 = 2 * (3w + 3 + w)
Now, let's simplify the equation by combining like terms:
46 = 2 * (4w + 3)
Next, let's distribute the 2 on the right side of the equation:
46 = 8w + 6
To isolate the variable, subtract 6 from both sides of the equation:
46 - 6 = 8w
40 = 8w
Finally, divide both sides of the equation by 8 to solve for w:
40/8 = w
5 = w
Therefore, the width of the rectangle is 5 centimeters.
To find the length of the rectangle, substitute the value of w into the expression for the length:
Length = 3w + 3 = 3(5) + 3 = 15 + 3 = 18
Hence, the dimensions of the rectangle are:
Width = 5 centimeters
Length = 18 centimeters
To find the dimensions of the rectangle, let's denote the width as 'W' and the length as 'L'.
According to the given information, the length of the rectangle is 3 centimeters more than 3 times the width: L = 3W + 3.
The perimeter of a rectangle is calculated by adding the lengths of all its sides. Since a rectangle has two pairs of equal sides, the formula for perimeter is: P = 2L + 2W.
Substituting the values we have:
46 = 2(3W + 3) + 2W.
Simplifying the equation:
46 = 6W + 6 + 2W,
46 = 8W + 6.
To isolate W, subtract 6 from both sides:
40 = 8W.
Dividing both sides by 8:
W = 5.
Now we can find the length by substituting W back into the equation:
L = 3W + 3,
L = 3(5) + 3,
L = 15 + 3,
L = 18.
Therefore, the dimensions of the rectangle are width = 5 centimeters and length = 18 centimeters.